一些奇奇怪怪的过题思路
Posted
tags:
篇首语：本文由小常识网(cha138.com)小编为大家整理，主要介绍了一些奇奇怪怪的过题思路相关的知识，希望对你有一定的参考价值。
最近考了几次试，做完之后发现自己还是缺乏思维精度和深度……在此把一些奇怪的思路记下来……
随
题意大概就是拿了一堆数取来取去，这些数在一个模数意义下做乘法，求出操作后取值的期望。
首先，找到这个模数的原根（鬼知道为什么现在出来了），然后就把这些乘法变成加法，然后就是矩阵一通乱搞……
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int maxn=1005,MOD=(int)1e9+7; 7 long long qpow(long long x,int tim,int Module) 8 { 9 long long tmp=1; 10 for(;tim;tim>>=1,x=x*x%Module) 11 if(tim&1)tmp=tmp*x%Module; 12 return tmp; 13 } 14 int getroot(int x) 15 { 16 for(int i=1;i<=x;i++) 17 { 18 int val=1;bool yes=1; 19 for(int j=1;j<x-1;j++) 20 { 21 val=val*1ll*i%x; 22 if(val==1) 23 { 24 yes=0; 25 break; 26 } 27 } 28 if(yes)return i; 29 } 30 } 31 int n,m,mod,powe[maxn],III[maxn],cnt[maxn],Probablities[33][maxn],f[2][maxn]; 32 void moduleadd(int &a,int b) 33 { 34 a+=b;if(a>MOD)a-=MOD; 35 } 36 int haha() 37 { 38 scanf("%d%d%d",&n,&m,&mod); 39 int rt=getroot(mod);powe[0]=1; 40 for(int i=1;i<=mod;i++)powe[i]=powe[i-1]*1ll*rt%mod; 41 int mod2=mod-1; 42 for(int i=0;i<mod2;i++)III[powe[i]]=i; 43 for(int i=1;i<=n;i++) 44 { 45 int x;scanf("%d",&x); 46 cnt[III[x]]++; 47 } 48 int Inv=qpow(n,MOD-2,MOD); 49 for(int i=0;i<mod2;i++)Probablities[0][i]=Inv*1ll*cnt[i]%MOD; 50 for(int i=1;i<=32;i++) 51 for(int j=0;j<mod2;j++) 52 for(int k=0;k<mod2;k++)moduleadd(Probablities[i][(j+k)%mod2],Probablities[i-1][j]*1ll*Probablities[i-1][k]%MOD); 53 f[0][0]=1; 54 for(int i=0;m;m>>=1,i++) 55 if(m&1) 56 { 57 for(int j=0;j<mod2;j++)f[1][j]=0; 58 for(int j=0;j<mod2;j++) 59 for(int k=0;k<mod2;k++)moduleadd(f[1][(k+j)%mod2],f[0][j]*1ll*Probablities[i][k]%MOD); 60 for(int j=0;j<mod2;j++)f[0][j]=f[1][j]; 61 } 62 int ans=0; 63 for(int i=0;i<mod2;i++)moduleadd(ans,f[0][i]*1ll*powe[i]%MOD); 64 printf("%d\\n",ans); 65 } 66 int sb=haha(); 67 int main(){;}
题
给出一大堆限制条件，问有多少种走回原点方法。
就是个分类讨论卡特兰数……（然而并没看出来）但是有种情况诡异的很……就是为2的时候……那个递推只能用恶心人来形容……
1 #include<iostream> 2 #include<cstring> 3 #include<cstdio> 4 using namespace std; 5 const int maxn=100005,mod=(int)1e9+7; 6 long long C[maxn]={1}; 7 long long qpow(long long x,int tim) 8 { 9 long long tmp=1; 10 for(;tim;tim>>=1,x=x*x%mod) 11 if(tim&1)tmp=tmp*x%mod; 12 return tmp; 13 } 14 long long f[maxn]={1}; 15 int haha() 16 { 17 int n,typ;scanf("%d%d",&n,&typ);long long ans=0,c=1; 18 for(int i=1;i<=n;i++)C[i]=C[i-1]*(4*(i+1)-6)%mod*qpow(i+1,mod-2)%mod; 19 switch(typ) 20 { 21 case 1:printf("%lld\\n",C[n>>1]);break; 22 case 0:for(int i=0;i<=n;i+=2) 23 { 24 ans+=c*C[i>>1]%mod*((i>>1)+1)%mod*C[(n-i)>>1]%mod*((n-i>>1)+1)%mod; 25 ans%=mod; 26 c=c*(n-i)%mod*(n-i-1)%mod*qpow(i+1,mod-2)%mod*qpow(i+2,mod-2)%mod; 27 } 28 printf("%lld\\n",ans);break; 29 case 3:for(int i=0;i<=n;i+=2) 30 { 31 ans+=c*C[i>>1]%mod*C[(n-i)>>1]%mod; 32 ans%=mod; 33 c=c*(n-i)%mod*(n-i-1)%mod*qpow(i+1,mod-2)%mod*qpow(i+2,mod-2)%mod; 34 } 35 printf("%lld\\n",ans);break; 36 case 2:for(int i=2;i<=n;i+=2) 37 for(int j=0;j<=i;j+=2)f[i]=(f[i]+4*f[i-j]*C[(j>>1)-1])%mod; 38 printf("%lld\\n",f[n]);break; 39 } 40 } 41 int sb=haha(); 42 int main(){;}
找硬币
找出一个序列使得前后项互为倍数，而且这个序列支付另一个序列花费硬币数最少。
马丹秦九韶都不会写给跪了……
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int prime[]={2,3,5,7,11,13,17,19,23,29,31,37,41,43,47,53,59,61,67,71,73,79,83,89,97,101,103,107,109,113,127,131,137,139,149,151,157,163,167,173,179,181,191,193,197,199,211,223,227,229,233,239,241,251,257,263,269,271,277,281,283,293,307,311,313,317,331,337,347,349,353,359,367,373,379,383,389,397,401,409,419,421,431,433,439,443,449,457,461,463,467,479,487,491,499,503,509,521,523,541,547,557,563,569,571,577,587,593,599,601,607,613,617,619,631,641,643,647,653,659,661,673,677,683,691,701,709,719,727,733,739,743,751,757,761,769,773,787,797,809,811,821,823,827,829,839,853,857,859,863,877,881,883,887,907,911,919,929,937,941,947,953,967,971,977,983,991,997,1009,1013,1019,1021,1031,1033,1039,1049,1051,1061,1063,1069,1087,1091,1093,1097,1103,1109,1117,1123,1129,1151,1153,1163,1171,1181,1187,1193,1201,1213,1217,1223,1229,1231,1237,1249,1259,1277,1279,1283,1289,1291,1297,1301,1303,1307,1319,1321,1327,1361,1367,1373,1381,1399,1409,1423,1427,1429,1433,1439,1447,1451,1453,1459,1471,1481,1483,1487,1489,1493,1499,1511,1523,1531,1543,1549,1553,1559,1567,1571,1579,1583,1597,1601,1607,1609,1613,1619,1621,1627,1637,1657,1663,1667,1669,1693,1697,1699,1709,1721,1723,1733,1741,1747,1753,1759,1777,1783,1787,1789,1801,1811,1823,1831,1847,1861,1867,1871,1873,1877,1879,1889,1901,1907,1913,1931,1933,1949,1951,1973,1979,1987,1993,1997,1999,2003,2011,2017,2027,2029,2039,2053,2063,2069,2081,2083,2087,2089,2099,2111,2113,2129,2131,2137,2141,2143,2153,2161,2179,2203,2207,2213,2221,2237,2239,2243,2251,2267,2269,2273,2281,2287,2293,2297,2309,2311,2333,2339,2341,2347,2351,2357,2371,2377,2381,2383,2389,2393,2399,2411,2417,2423,2437,2441,2447,2459,2467,2473,2477,2503,2521,2531,2539,2543,2549,2551,2557,2579,2591,2593,2609,2617,2621,2633,2647,2657,2659,2663,2671,2677,2683,2687,2689,2693,2699,2707,2711,2713,2719,2729,2731,2741,2749,2753,2767,2777,2789,2791,2797,2801,2803,2819,2833,2837,2843,2851,2857,2861,2879,2887,2897,2903,2909,2917,2927,2939,2953,2957,2963,2969,2971,2999,3001,3011,3019,3023,3037,3041,3049,3061,3067,3079,3083,3089,3109,3119,3121,3137,3163,3167,3169,3181,3187,3191,3203,3209,3217,3221,3229,3251,3253,3257,3259,3271,3299,3301,3307,3313,3319,3323,3329,3331,3343,3347,3359,3361,3371,3373,3389,3391,3407,3413,3433,3449,3457,3461,3463,3467,3469,3491,3499,3511,3517,3527,3529,3533,3539,3541,3547,3557,3559,3571,3581,3583,3593,3607,3613,3617,3623,3631,3637,3643,3659,3671,3673,3677,3691,3697,3701,3709,3719,3727,3733,3739,3761,3767,3769,3779,3793,3797,3803,3821,3823,3833,3847,3851,3853,3863,3877,3881,3889,3907,3911,3917,3919,3923,3929,3931,3943,3947,3967,3989,4001,4003,4007,4013,4019,4021,4027,4049,4051,4057,4073,4079,4091,4093,4099,4111,4127,4129,4133,4139,4153,4157,4159,4177,4201,4211,4217,4219,4229,4231,4241,4243,4253,4259,4261,4271,4273,4283,4289,4297,4327,4337,4339,4349,4357,4363,4373,4391,4397,4409,4421,4423,4441,4447,4451,4457,4463,4481,4483,4493,4507,4513,4517,4519,4523,4547,4549,4561,4567,4583,4591,4597,4603,4621,4637,4639,4643,4649,4651,4657,4663,4673,4679,4691,4703,4721,4723,4729,4733,4751,4759,4783,4787,4789,4793,4799,4801,4813,4817,4831,4861,4871,4877,4889,4903,4909,4919,4931,4933,4937,4943,4951,4957,4967,4969,4973,4987,4993,4999,5003,5009,5011,5021,5023,5039,5051,5059,5077,5081,5087,5099,5101,5107,5113,5119,5147,5153,5167,5171,5179,5189,5197,5209,5227,5231,5233,5237,5261,5273,5279,5281,5297,5303,5309,5323,5333,5347,5351,5381,5387,5393,5399,5407,5413,5417,5419,5431,5437,5441,5443,5449,5471,5477,5479,5483,5501,5503,5507,5519,5521,5527,5531,5557,5563,5569,5573,5581,5591,5623,5639,5641,5647,5651,5653,5657,5659,5669,5683,5689,5693,5701,5711,5717,5737,5741,5743,5749,5779,5783,5791,5801,5807,5813,5821,5827,5839,5843,5849,5851,5857,5861,5867,5869,5879,5881,5897,5903,5923,5927,5939,5953,5981,5987,6007,6011,6029,6037,6043,6047,6053,6067,6073,6079,6089,6091,6101,6113,6121,6131,6133,6143,6151,6163,6173,6197,6199,6203,6211,6217,6221,6229,6247,6257,6263,6269,6271,6277,6287,6299,6301,6311,6317,6323,6329,6337,6343,6353,6359,6361,6367,6373,6379,6389,6397,6421,6427,6449,6451,6469,6473,6481,6491,6521,6529,6547,6551,6553,6563,6569,6571,6577,6581,6599,6607,6619,6637,6653,6659,6661,6673,6679,6689,6691,6701,6703,6709,6719,6733,6737,6761,6763,6779,6781,6791,6793,6803,6823,6827,6829,6833,6841,6857,6863,6869,6871,6883,6899,6907,6911,6917,6947,6949,6959,6961,6967,6971,6977,6983,6991,6997,7001,7013,7019,7027,7039,7043,7057,7069,7079,7103,7109,7121,7127,7129,7151,7159,7177,7187,7193,7207,7211,7213,7219,7229,7237,7243,7247,7253,7283,7297,7307,7309,7321,7331,7333,7349,7351,7369,7393,7411,7417,7433,7451,7457,7459,7477,7481,7487,7489,7499,7507,7517,7523,7529,7537,7541,7547,7549,7559,7561,7573,7577,7583,7589,7591,7603,7607,7621,7639,7643,7649,7669,7673,7681,7687,7691,7699,7703,7717,7723,7727,7741,7753,7757,7759,7789,7793,7817,7823,7829,7841,7853,7867,7873,7877,7879,7883,7901,7907,7919,7927,7933,7937,7949,7951,7963,7993,8009,8011,8017,8039,8053,8059,8069,8081,8087,8089,8093,8101,8111,8117,8123,8147,8161,8167,8171,8179,8191,8209,8219,8221,8231,8233,8237,8243,8263,8269,8273,8287,8291,8293,8297,8311,8317,8329,8353,8363,8369,8377,8387,8389,8419,8423,8429,8431,8443,8447,8461,8467,8501,8513,8521,8527,8537,8539,8543,8563,8573,8581,8597,8599,8609,8623,8627,8629,8641,8647,8663,8669,8677,8681,8689,8693,8699,8707,8713,8719,8731,8737,8741,8747,8753,8761,8779,8783,8803,8807,8819,8821,8831,8837,8839,8849,8861,8863,8867,8887,8893,8923,8929,8933,8941,8951,8963,8969,8971,8999,9001,9007,9011,9013,9029,9041,9043,9049,9059,9067,9091,9103,9109,9127,9133,9137,9151,9157,9161,9173,9181,9187,9199,9203,9209,9221,9227,9239,9241,9257,9277,9281,9283,9293,9311,9319,9323,9337,9341,9343,9349,9371,9377,9391,9397,9403,9413,9419,9421,9431,9433,9437,9439,9461,9463,9467,9473,9479,9491,9497,9511,9521,9533,9539,9547,9551,9587,9601,9613,9619,9623,9629,9631,9643,9649,9661,9677,9679,9689,9697,9719,9721,9733,9739,9743,9749,9767,9769,9781,9787,9791,9803,9811,9817,9829,9833,9839,9851,9857,9859,9871,9883,9887,9901,9907,9923,9929,9931,9941,9949,9967,9973,10007,10009,10037,10039,10061,10067,10069,10079,10091,10093,10099,10103,10111,10133,10139,10141,10151,10159,10163,10169,10177,10181,10193,10211,10223,10243,10247,10253,10259,10267,10271,10273,10289,10301,10303,10313,10321,10331,10333,10337,10343,10357,10369,10391,10399,10427,10429,10433,10453,10457,10459,10463,10477,10487,10499,10501,10513,10529,10531,10559,10567,10589,10597,10601,10607,10613,10627,10631,10639,10651,10657,10663,10667,10687,10691,10709,10711,10723,10729,10733,10739,10753,10771,10781,10789,10799,10831,10837,10847,10853,10859,10861,10867,10883,10889,10891,10903,10909,10937,10939,10949,10957,10973,10979,10987,10993,11003,11027,11047,11057,11059,11069,11071,11083,11087,11093,11113,11117,11119,11131,11149,11159,11161,11171,11173,11177,11197,11213,11239,11243,11251,11257,11261,11273,11279,11287,11299,11311,11317,11321,11329,11351,11353,11369,11383,11393,11399,11411,11423,11437,11443,11447,11467,11471,11483,11489,11491,11497,11503,11519,11527,11549,11551,11579,11587,11593,11597,11617,11621,11633,11657,11677,11681,11689,11699,11701,11717,11719,11731,11743,11777,11779,11783,11789,11801,11807,11813,11821,11827,11831,11833,11839,11863,11867,11887,11897,11903,11909,11923,11927,11933,11939,11941,11953,11959,11969,11971,11981,11987,12007,12011,12037,12041,12043,12049,12071,12073,12097,12101,12107,12109,12113,12119,12143,12149,12157,12161,12163,12197,12203,12211,12227,12239,12241,12251,12253,12263,12269,12277,12281,12289,12301,12323,12329,12343,12347,12373,12377,12379,12391,12401,12409,12413,12421,12433,12437,12451,12457,12473,12479,12487,12491,12497,12503,12511,12517,12527,12539,12541,12547,12553,12569,12577,12583,12589,12601,12611,12613,12619,12637,12641,12647,12653,12659,12671,12689,12697,12703,12713,12721,12739,12743,12757,12763,12781,12791,12799,12809,12821,12823,12829,12841,12853,12889,12893,12899,12907,12911,12917,12919,12923,12941,12953,12959,12967,12973,12979,12983,13001,13003,13007,13009,13033,13037,13043,13049,13063,13093,13099,13103,13109,13121,13127,13147,13151,13159,13163,13171,13177,13183,13187,13217,13219,13229,13241,13249,13259,13267,13291,13297,13309,13313,13327,13331,13337,13339,13367,13381,13397,13399,13411,13417,13421,13441,13451,13457,13463,13469,13477,13487,13499,13513,13523,13537,13553,13567,13577,13591,13597,13613,13619,13627,13633,13649,13669,13679,13681,13687,13691,13693,13697,13709,13711,13721,13723,13729,13751,13757,13759,13763,13781,13789,13799,13807,13829,13831,13841,13859,13873,13877,13879,13883,13901,13903,13907,13913,13921,13931,13933,13963,13967,13997,13999,14009,14011,14029,14033,14051,14057,14071,14081,14083,14087,14107,14143,14149,14153,14159,14173,14177,14197,14207,14221,14243,14249,14251,14281,14293,14303,14321,14323,14327,14341,14347,14369,14387,14389,14401,14407,14411,14419,14423,14431,14437,14447,14449,14461,14479,14489,14503,14519,14533,14537,14543,14549,14551,14557,14561,14563,14591,14593,14621,14627,14629,14633,14639,14653,14657,14669,14683,14699,14713,14717,14723,14731,14737,14741,14747,14753,14759,14767,14771,14779,14783,14797,14813,14821,14827,14831,14843,14851,14867,14869,14879,14887,14891,14897,14923,14929,14939,14947,14951,14957,14969,14983,15013,15017,15031,15053,15061,15073,15077,15083,15091,15101,15107,15121,15131,15137,15139,15149,15161,15173,15187,15193,15199,15217,15227,15233,15241,15259,15263,15269,15271,15277,15287,15289,15299,15307,15313,15319,15329,15331,15349,15359,15361,15373,15377,15383,15391,15401,15413,15427,15439,15443,15451,15461,15467,15473,15493,15497,15511,15527,15541,15551,15559,15569,15581,15583,15601,15607,15619,15629,15641,15643,15647,15649,15661,15667,15671,15679,15683,15727,15731,15733,15737,15739,15749,15761,15767,15773,15787,15791,15797,15803,15809,15817,15823,15859,15877,15881,15887,15889,15901,15907,15913,15919,15923,15937,15959,15971,15973,15991,16001,16007,16033,16057,16061,16063,16067,16069,16073,16087,16091,16097,16103,16111,16127,16139,16141,16183,16187,16189,16193,16217,16223,16229,16231,16249,16253,16267,16273,16301,16319,16333,16339,16349,16361,16363,16369,16381,16411,16417,16421,16427,16433,16447,16451,16453,16477,16481,16487,16493,16519,16529,16547,16553,16561,16567,16573,16603,16607,16619,16631,16633,16649,16651,16657,16661,16673,16691,16693,16699,16703,16729,16741,16747,16759,16763,16787,16811,16823,16829,16831,16843,16871,16879,16883,16889,16901,16903,16921,16927,16931,16937,16943,16963,16979,16981,16987,16993,17011,17021,17027,17029,17033,17041,17047,17053,17077,17093,17099,17107,17117,17123,17137,17159,17167,17183,17189,17191,17203,17207,17209,17231,17239,17257,17291,17293,17299,17317,17321,17327,17333,17341,17351,17359,17377,17383,17387,17389,17393,17401,17417,17419,17431,17443,17449,17467,17471,17477,17483,17489,17491,17497,17509,17519,17539,17551,17569,17573,17579,17581,17597,17599,17609,17623,17627,17657,17659,17669,17681,17683,17707,17713,17729,17737,17747,17749,17761,17783,17789,17791,17807,17827,17837,17839,17851,17863,17881,17891,17903,17909,17911,17921,17923,17929,17939,17957,17959,17971,17977,17981,17987,17989,18013,18041,18043,18047,18049,18059,18061,18077,18089,18097,18119,18121,18127,18131,18133,18143,18149,18169,18181,18191,18199,18211,18217,18223,18229,18233,18251,18253,18257,18269,18287,18289,18301,18307,18311,18313,18329,18341,18353,18367,18371,18379,18397,18401,18413,18427,18433,18439,18443,18451,18457,18461,18481,18493,18503,18517,18521,18523,18539,18541,18553,18583,18587,18593,18617,18637,18661,18671,18679,18691,18701,18713,18719,18731,18743,18749,18757,18773,18787,18793,18797,18803,18839,18859,18869,18899,18911,18913,18917,18919,18947,18959,18973,18979,19001,19009,19013,19031,19037,19051,19069,19073,19079,19081,19087,19121,19139,19141,19157,19163,19181,19183,19207,19211,19213,19219,19231,19237,19249,19259,19267,19273,19289,19301,19309,19319,19333,19373,19379,19381,19387,19391,19403,19417,19421,19423,19427,19429,19433,19441,19447,19457,19463,19469,19471,19477,19483,19489,19501,19507,19531,19541,19543,19553,19559,19571,19577,19583,19597,19603,19609,19661,19681,19687,19697,19699,19709,19717,19727,19739,19751,19753,19759,19763,19777,19793,19801,19813,19819,19841,19843,19853,19861,19867,19889,19891,19913,19919,19927,19937,19949,19961,19963,19973,19979,19991,19993,19997,20011,20021,20023,20029,20047,20051,20063,20071,20089,20101,20107,20113,20117,20123,20129,20143,20147,20149,20161,20173,20177,20183,20201,20219,20231,20233,20249,20261,20269,20287,20297,20323,20327,20333,20341,20347,20353,20357,20359,20369,20389,20393,20399,20407,20411,20431,20441,20443,20477,20479,20483,20507,20509,20521,20533,20543,20549,20551,20563,20593,20599,20611,20627,20639,20641,20663,20681,20693,20707,20717,20719,20731,20743,20747,20749,20753,20759,20771,20773,20789,20807,20809,20849,20857,20873,20879,20887,20897,20899,20903,20921,20929,20939,20947,20959,20963,20981,20983,21001,21011,21013,21017,21019,21023,21031,21059,21061,21067,21089,21101,21107,21121,21139,21143,21149,21157,21163,21169,21179,21187,21191,21193,21211,21221,21227,21247,21269,21277,21283,21313,21317,21319,21323,21341,21347,21377,21379,21383,21391,21397,21401,21407,21419,21433,21467,21481,21487,21491,21493,21499,21503,21517,21521,21523,21529,21557,21559,21563,21569,21577,21587,21589,21599,21601,21611,21613,21617,21647,21649,21661,21673,21683,21701,21713,21727,21737,21739,21751,21757,21767,21773,21787,21799,21803,21817,21821,21839,21841,21851,21859,21863,21871,21881,21893,21911,21929,21937,21943,21961,21977,21991,21997,22003,22013,22027,22031,22037,22039,22051,22063,22067,22073,22079,22091,22093,22109,22111,22123,22129,22133,22147,22153,22157,22159,22171,22189,22193,22229,22247,22259,22271,22273,22277,22279,22283,22291,22303,22307,22343,22349,22367,22369,22381,22391,22397,22409,22433,22441,22447,22453,22469,22481,22483,22501,22511,22531,22541,22543,22549,22567,22571,22573,22613,22619,22621,22637,22639,22643,22651,22669,22679,22691,22697,22699,22709,22717,22721,22727,22739,22741,22751,22769,22777,22783,22787,22807,22811,22817,22853,22859,22861,22871,22877,22901,22907,22921,22937,22943,22961,22963,22973,22993,23003,23011,23017,23021,23027,23029,23039,23041,23053,23057,23059,23063,23071,23081,23087,23099,23117,23131,23143,23159,23167,23173,23189,23197,23201,23203,23209,23227,23251,23269,23279,23291,23293,23297,23311,23321,23327,23333,23339,23357,23369,23371,23399,23417,23431,23447,23459,23473,23497,23509,23531,23537,23539,23549,23557,23561,23563,23567,23581,23593,23599,23603,23609,23623,23627,23629,23633,23663,23669,23671,23677,23687,23689,23719,23741,23743,23747,23753,23761,23767,23773,23789,23801,23813,23819,23827,23831,23833,23857,23869,23873,23879,23887,23893,23899,23909,23911,23917,23929,23957,23971,23977,23981,23993,24001,24007,24019,24023,24029,24043,24049,24061,24071,24077,24083,24091,24097,24103,24107,24109,24113,24121,24133,24137,24151,24169,24179,24181,24197,24203,24223,24229,24239,24247,24251,24281,24317,24329,24337,24359,24371,24373,24379,24391,24407,24413,24419,24421,24439,24443,24469,24473,24481,24499,24509,24517,24527,24533,24547,24551,24571,24593,24611,24623,24631,24659,24671,24677,24683,24691,24697,24709,24733,24749,24763,24767,24781,24793,24799,24809,24821,24841,24847,24851,24859,24877,24889,24907,24917,24919,24923,24943,24953,24967,24971,24977,24979,24989,25013,25031,25033,25037,25057,25073,25087,25097,25111,25117,25121,25127,25147,25153,25163,25169,25171,25183,25189,25219,25229,25237,25243,25247,25253,25261,25301,25303,25307,25309,25321,25339,25343,25349,25357,25367,25373,25391,25409,25411,25423,25439,25447,25453,25457,25463,25469,25471,25523,25537,25541,25561,25577,25579,25583,25589,25601,25603,25609,25621,25633,25639,25643,25657,25667,25673,25679,25693,25703,25717,25733,25741,25747,25759,25763,25771,25793,25799,25801,25819,25841,25847,25849,25867,25873,25889,25903,25913,25919,25931,25933,25939,25943,25951,25969,25981,25997,25999,26003,26017,26021,26029,26041,26053,26083,26099,26107,26111,26113,26119,26141,26153,26161,26171,26177,26183,26189,26203,26209,26227,26237,26249,26251,26261,26263,26267,26293,26297,26309,26317,26321,26339,26347,26357,26371,26387,26393,26399,26407,26417,26423,26431,26437,26449,26459,26479,26489,26497,26501,26513,26539,26557,26561,26573,26591,26597,26627,26633,26641,26647,26669,26681,26683,26687,26693,26699,26701,26711,26713,26717,26723,26729,26731,26737,26759,26777,26783,26801,26813,26821,26833,26839,26849,26861,26863,26879,26881,26891,26893,26903,26921,26927,26947,26951,26953,26959,26981,26987,26993,27011,27017,27031,27043,27059,27061,27067,27073,27077,27091,27103,27107,27109,27127,27143,27179,27191,27197,27211,27239,27241,27253,27259,27271,27277,27281,27283,27299,27329,27337,27361,27367,27397,27407,27409,27427,27431,27437,27449,27457,27479,27481,27487,27509,27527,27529,27539,27541,27551,27581,27583,27611,27617,27631,27647,27653,27673,27689,27691,27697,27701,27733,27737,27739,27743,27749,27751,27763,27767,27773,27779,27791,27793,27799,27803,27809,27817,27823,27827,27847,27851,27883,27893,27901,27917,27919,27941,27943,27947,27953,27961,27967,27983,27997,28001,28019,28027,28031,28051,28057,28069,28081,28087,28097,28099,28109,28111,28123,28151,28163,28181,28183,28201,28211,28219,28229,28277,28279,28283,28289,28297,28307,28309,28319,28349,28351,28387,28393,28403,28409,28411,28429,28433,28439,28447,28463,28477,28493,28499,28513,28517,28537,28541,28547,28549,28559,28571,28573,28579,28591,28597,28603,28607,28619,28621,28627,28631,28643,28649,28657,28661,28663,28669,28687,28697,28703,28711,28723,28729,28751,28753,28759,28771,28789,28793,28807,28813,28817,28837,28843,28859,28867,28871,28879,28901,28909,28921,28927,28933,28949,28961,28979,29009,29017,29021,29023,29027,29033,29059,29063,29077,29101,29123,29129,29131,29137,29147,29153,29167,29173,29179,29191,29201,29207,29209,29221,29231,29243,29251,29269,29287,29297,29303,29311,29327,29333,29339,29347,29363,29383,29387,29389,29399,29401,29411,29423,29429,29437,29443,29453,29473,29483,29501,29527,29531,29537,29567,29569,29573,29581,29587,29599,29611,29629,29633,29641,29663,29669,29671,29683,29717,29723,29741,29753,29759,29761,29789,29803,29819,29833,29837,29851,29863,29867,29873,29879,29881,29917,29921,29927,29947,29959,29983,29989,30011,30013,30029,30047,30059,30071,30089,30091,30097,30103,30109,30113,30119,30133,30137,30139,30161,30169,30181,30187,30197,30203,30211,30223,30241,30253,30259,30269,30271,30293,30307,30313,30319,30323,30341,30347,30367,30389,30391,30403,30427,30431,30449,30467,30469,30491,30493,30497,30509,30517,30529,30539,30553,30557,30559,30577,30593,30631,30637,30643,30649,30661,30671,30677,30689,30697,30703,30707,30713,30727,30757,30763,30773,30781,30803,30809,30817,30829,30839,30841,30851,30853,30859,30869,30871,30881,30893,30911,30931,30937,30941,30949,30971,30977,30983,31013,31019,31033,31039,31051,31063,31069,31079,31081,31091,31121,31123,31139,31147,31151,31153,31159,31177,31181,31183,31189,31193,31219,31223,31231,31237,31247,31249,31253,31259,31267,31271,31277,31307,31319,31321,31327,31333,31337,31357,31379,31387,31391,31393,31397,31469,31477,31481,31489,31511,31513,31517,31531,31541,31543,31547,31567,31573,31583,31601,31607,31627,31643,31649,31657,31663,31667,31687,31699,31721,31723,31727,31729,31741,31751,31769,31771,31793,31799,31817,31847,31849,31859,31873,31883,31891,31907,31957,31963,31973,31981,31991,32003,32009,32027,32029,32051,32057,32059,32063,32069,32077,32083,32089,32099,32117,32119,32141,32143,32159,32173,32183,32189,32191,32203,32213,32233,32237,32251,32257,32261,32297,32299,32303,32309,32321,32323,32327,32341,32353,32359,32363,32369,32371,32377,32381,32401,32411,32413,32423,32429,32441,32443,32467,32479,32491,32497,32503,32507,32531,32533,32537,32561,32563,32569,32573,32579,32587,32603,32609,32611,32621,32633,32647,32653,32687,32693,32707,32713,32717,32719,32749,32771,32779,32783,32789,32797,32801,32803,32831,32833,32839,32843,32869,32887,32909,32911,32917,32933,32939,32941,32957,32969,32971,32983,32987,32993,32999,33013,33023,33029,33037,33049,33053,33071,33073,33083,33091,33107,33113,33119,33149,33151,33161,33179,33181,33191,33199,33203,33211,33223,33247,33287,33289,33301,33311,33317,33329,33331,33343,33347,33349,33353,33359,33377,33391,33403,33409,33413,33427,33457,33461,33469,33479,33487,33493,33503,33521,33529,33533,33547,33563,33569,33577,33581,33587,33589,33599,33601,33613,33617,33619,33623,33629,33637,33641,33647,33679,33703,33713,33721,33739,33749,33751,33757,33767,33769,33773,33791,33797,33809,33811,33827,33829,33851,33857,33863,33871,33889,33893,33911,33923,33931,33937,33941,33961,33967,33997,34019,34031,34033,34039,34057,34061,34123,34127,34129,34141,34147,34157,34159,34171,34183,34211,34213,34217,34231,34253,34259,34261,34267,34273,34283,34297,34301,34303,34313,34319,34327,34337,34351,34361,34367,34369,34381,34403,34421,34429,34439,34457,34469,34471,34483,34487,34499,34501,34511,34513,34519,34537,34543,34549,34583,34589,34591,34603,34607,34613,34631,34649,34651,34667,34673,34679,34687,34693,34703,34721,34729,34739,34747,34757,34759,34763,34781,34807,34819,34841,34843,34847,34849,34871,34877,34883,34897,34913,34919,34939,34949,34961,34963,34981,35023,35027,35051,35053,35059,35069,35081,35083,35089,35099,35107,35111,35117,35129,35141,35149,35153,35159,35171,35201,35221,35227,35251,35257,35267,35279,35281,35291,35311,35317,35323,35327,35339,35353,35363,35381,35393,35401,35407,35419,35423,35437,35447,35449,35461,35491,35507,35509,35521,35527,35531,35533,35537,35543,35569,35573,35591,35593,35597,35603,35617,35671,35677,35729,35731,35747,35753,35759,35771,35797,35801,35803,35809,35831,35837,35839,35851,35863,35869,35879,35897,35899,35911,35923,35933,35951,35963,35969,35977,35983,35993,35999,36007,36011,36013,36017,36037,36061,36067,36073,36083,36097,36107,36109,36131,36137,36151,36161,36187,36191,36209,36217,36229,36241,36251,36263,36269,36277,36293,36299,36307,36313,36319,36341,36343,36353,36373,36383,36389,36433,36451,36457,36467,36469,36473,36479,36493,36497,36523,36527,36529,36541,36551,36559,36563,36571,36583,36587,36599,36607,36629,36637,36643,36653,36671,36677,36683,36691,36697,36709,36713,36721,36739,36749,36761,36767,36779,36781,36787,36791,36793,36809,36821,36833,36847,36857,36871,36877,36887,36899,36901,36913,36919,36923,36929,36931,36943,36947,36973,36979,36997,37003,37013,37019,37021,37039,37049,37057,37061,37087,37097,37117,37123,37139,37159,37171,37181,37189,37199,37201,37217,37223,37243,37253,37273,37277,37307,37309,37313,37321,37337,37339,37357,37361,37363,37369,37379,37397,37409,37423,37441,37447,37463,37483,37489,37493,37501,37507,37511,37517,37529,37537,37547,37549,37561,37567,37571,37573,37579,37589,37591,37607,37619,37633,37643,37649,37657,37663,37691,37693,37699,37717,37747,37781,37783,37799,37811,37813,37831,37847,37853,37861,37871,37879,37889,37897,37907,37951,37957,37963,37967,37987,37991,37993,37997,38011,38039,38047,38053,38069,38083,38113,38119,38149,38153,38167,38177,38183,38189,38197,38201,38219,38231,38237,38239,38261,38273,38281,38287,38299,38303,38317,38321,38327,38329,38333,38351,38371,38377,38393,38431,38447,38449,38453,38459,38461,38501,38543,38557,38561,38567,38569,38593,38603,38609,38611,38629,38639,38651,38653,38669,38671,38677,38693,38699,38707,38711,38713,38723,38729,38737,38747,38749,38767,38783,38791,38803,38821,38833,38839,38851,38861,38867,38873,38891,38903,38917,38921,38923,38933,38953,38959,38971,38977,38993,39019,39023,39041,39043,39047,39079,39089,39097,39103,39107,39113,39119,39133,39139,39157,39161,39163,39181,39191,39199,39209,39217,39227,39229,39233,39239,39241,39251,39293,39301,39313,39317,39323,39341,39343,39359,39367,39371,39373,39383,39397,39409,39419,39439,39443,39451,39461,39499,39503,39509,39511,39521,39541,39551,39563,39569,39581,39607,39619,39623,39631,39659,39667,39671,39679,39703,39709,39719,39727,39733,39749,39761,39769,39779,39791,39799,39821,39827,39829,39839,39841,39847,39857,39863,39869,39877,39883,39887,39901,39929,39937,39953,39971,39979,39983,39989,40009,40013,40031,40037,40039,40063,40087,40093,40099,40111,40123,40127,40129,40151,40153,40163,40169,40177,40189,40193,40213,40231,40237,40241,40253,40277,40283,40289,40343,40351,40357,40361,40387,40423,40427,40429,40433,40459,40471,40483,40487,40493,40499,40507,40519,40529,40531,40543,40559,40577,40583,40591,40597,40609,40627,40637,40639,40693,40697,40699,40709,40739,40751,40759,40763,40771,40787,40801,40813,40819,40823,40829,40841,40847,40849,40853,40867,40879,40883,40897,40903,40927,40933,40939,40949,40961,40973,40993,41011,41017,41023,41039,41047,41051,41057,41077,41081,41113,41117,41131,41141,41143,41149,41161,41177,41179,41183,41189,41201,41203,41213,41221,41227,41231,41233,41243,41257,41263,41269,41281,41299,41333,41341,41351,41357,41381,41387,41389,41399,41411,41413,41443,41453,41467,41479,41491,41507,41513,41519,41521,41539,41543,41549,41579,41593,41597,41603,41609,41611,41617,41621,41627,41641,41647,41651,41659,41669,41681,41687,41719,41729,41737,41759,41761,41771,41777,41801,41809,41813,41843,41849,41851,41863,41879,41887,41893,41897,41903,41911,41927,41941,41947,41953,41957,41959,41969,41981,41983,41999,42013,42017,42019,42023,42043,42061,42071,42073,42083,42089,42101,42131,42139,42157,42169,42179,42181,42187,42193,42197,42209,42221,42223,42227,42239,42257,42281,42283,42293,42299,42307,42323,42331,42337,42349,42359,42373,42379,42391,42397,42403,42407,42409,42433,42437,42443,42451,42457,42461,42463,42467,42473,42487,42491,42499,42509,42533,42557,42569,42571,42577,42589,42611,42641,42643,42649,42667,42677,42683,42689,42697,42701,42703,42709,42719,42727,42737,42743,42751,42767,42773,42787,42793,42797,42821,42829,42839,42841,42853,42859,42863,42899,42901,42923,42929,42937,42943,42953,42961,42967,42979,42989,43003,43013,43019,43037,43049,43051,43063,43067,43093,43103,43117,43133,43151,43159,43177,43189,43201,43207,43223,43237,43261,43271,43283,43291,43313,43319,43321,43331,43391,43397,43399,43403,43411,43427,43441,43451,43457,43481,43487,43499,43517,43541,43543,43573,43577,43579,43591,43597,43607,43609,43613,43627,43633,43649,43651,43661,43669,43691,43711,43717,43721,43753,43759,43777,43781,43783,43787,43789,43793,43801,43853,43867,43889,43891,43913,43933,43943,43951,43961,43963,43969,43973,43987,43991,43997,44017,44021,44027,44029,44041,44053,44059,44071,44087,44089,44101,44111,44119,44123,44129,44131,44159,44171,44179,44189,44201,44203,44207,44221,44249,44257,44263,44267,44269,44273,44279,44281,44293,44351,44357,44371,44381,44383,44389,44417,44449,44453,44483,44491,44497,44501,44507,44519,44531,44533,44537,44543,44549,44563,44579,44587,44617,44621,44623,44633,44641,44647,44651,44657,44683,44687,44699,44701,44711,44729,44741,44753,44771,44773,44777,44789,44797,44809,44819,44839,44843,44851,44867,44879,44887,44893,44909,44917,44927,44939,44953,44959,44963,44971,44983,44987,45007,45013,45053,45061,45077,45083,45119,45121,45127,45131,45137,45139,45161,45179,45181,45191,45197,45233,45247,45259,45263,45281,45289,45293,45307,45317,45319,45329,45337,45341,45343,45361,45377,45389,45403,45413,45427,45433,45439,45481,45491,45497,45503,45523,45533,45541,45553,45557,45569,45587,45589,45599,45613,45631,45641,45659,45667,45673,45677,45691,45697,45707,45737,45751,45757,45763,45767,45779,45817,45821,45823,45827,45833,45841,45853,45863,45869,45887,45893,45943,45949,45953,45959,45971,45979,45989,46021,46027,46049,46051,46061,46073,46091,46093,46099,46103,46133,46141,46147,46153,46171,46181,46183,46187,46199,46219,46229,46237,46261,46271,46273,46279,46301,46307,46309,46327,46337,46349,46351,46381,46399,46411,46439,46441,46447,46451,46457,46471,46477,46489,46499,46507,46511,46523,46549,46559,46567,46573,46589,46591,46601,46619,46633,46639,46643,46649,46663,46679,46681,46687,46691,46703,46723,46727,46747,46751,46757,46769,46771,46807,46811,46817,46819,46829,46831,46853,46861,46867,46877,46889,46901,46919,46933,46957,46993,46997,47017,47041,47051,47057,47059,47087,47093,47111,47119,47123,47129,47137,47143,47147,47149,47161,47189,47207,47221,47237,47251,47269,47279,47287,47293,47297,47303,47309,47317,47339,47351,47353,47363,47381,47387,47389,47407,47417,47419,47431,47441,47459,47491,47497,47501,47507,47513,47521,47527,47533,47543,47563,47569,47581,47591,47599,47609,47623,47629,47639,47653,47657,47659,47681,47699,47701,47711,47713,47717,47737,47741,47743,47777,47779,47791,47797,47807,47809,47819,47837,47843,47857,47869,47881,47903,47911,47917,47933,47939,47947,47951,47963,47969,47977,47981,48017,48023,48029,48049,48073,48079,48091,48109,48119,48121,48131,48157,48163,48179,48187,48193,48197,48221,48239,48247,48259,48271,48281,48299,48311,48313,48337,48341,48353,48371,48383,48397,48407,48409,48413,48437,48449,48463,48473,48479,48481,48487,48491,48497,48523,48527,48533,48539,48541,48563,48571,48589,48593,48611,48619,48623,48647,48649,48661,48673,48677,48679,48731,48733,48751,48757,48761,48767,48779,48781,48787,48799,48809,48817,48821,48823,48847,48857,48859,48869,48871,48883,48889,48907,48947,48953,48973,48989,48991,49003,49009,49019,49031,49033,49037,49043,49057,49069,49081,49103,49109,49117,49121,49123,49139,49157,49169,49171,49177,49193,49199,49201,49207,49211,49223,49253,49261,49277,49279,49297,49307,49331,49333,49339,49363,49367,49369,49391,49393,49409,49411,49417,49429,49433,49451,49459,49463,49477,49481,49499,49523,49529,49531,49537,49547,49549,49559,49597,49603,49613,49627,49633,49639,49663,49667,49669,49681,49697,49711,49727,49739,49741,49747,49757,49783,49787,49789,49801,49807,49811,49823,49831,49843,49853,49871,49877,49891,49919,49921,49927,49937,49939,49943,49957,49991,49993,49999,50021,50023,50033,50047,50051,50053,50069,50077,50087,50093,50101,50111,50119,50123,50129,50131,50147,50153,50159,50177,50207,50221,50227,50231,50261,50263,50273,50287,50291,50311,50321,50329,50333,50341,50359,50363,50377,50383,50387,50411,50417,50423,50441,50459,50461,50497,50503,50513,50527,50539,50543,50549,50551,50581,50587,50591,50593,50599,50627,50647,50651,50671,50683,50707,50723,50741,50753,50767,50773,50777,50789,50821,50833,50839,50849,50857,50867,50873,50891,50893,50909,50923,50929,50951,50957,50969,50971,50989,50993,51001,51031,51043,51047,51059,51061,51071,51109,51131,51133,51137,51151,51157,51169,51193,51197,51199,51203,51217,51229,51239,51241,51257,51263,51283,51287,51307,51329,51341,51343,51347,51349,51361,51383,51407,51413,51419,51421,51427,51431,51437,51439,51449,51461,51473,51479,51481,51487,51503,51511,51517,51521,51539,51551,51563,51577,51581,51593,51599,51607,51613,51631,51637,51647,51659,51673,51679,51683,51691,51713,51719,51721,51749,51767,51769,51787,51797,51803,51817,51827,51829,51839,51853,51859,51869,51871,51893,51899,51907,51913,51929,51941,51949,51971,51973,51977,51991,52009,52021,52027,52051,52057,52067,52069,52081,52103,52121,52127,52147,52153,52163,52177,52181,52183,52189,52201,52223,52237,52249,52253,52259,52267,52289,52291,52301,52313,52321,52361,52363,52369,52379,52387,52391,52433,52453,52457,52489,52501,52511,52517,52529,52541,52543,52553,52561,52567,52571,52579,52583,52609,52627,52631,52639,52667,52673,52691,52697,52709,52711,52721,52727,52733,52747,52757,52769,52783,52807,52813,52817,52837,52859,52861,52879,52883,52889,52901,52903,52919,52937,52951,52957,52963,52967,52973,52981,52999,53003,53017,53047,53051,53069,53077,53087,53089,53093,53101,53113,53117,53129,53147,53149,53161,53171,53173,53189,53197,53201,53231,53233,53239,53267,53269,53279,53281,53299,53309,53323,53327,53353,53359,53377,53381,53401,53407,53411,53419,53437,53441,53453,53479,53503,53507,53527,53549,53551,53569,53591,53593,53597,53609,53611,53617,53623,53629,53633,53639,53653,53657,53681,53693,53699,53717,53719,53731,53759,53773,53777,53783,53791,53813,53819,53831,53849,53857,53861,53881,53887,53891,53897,53899,53917,53923,53927,53939,53951,53959,53987,53993,54001,54011,54013,54037,54049,54059,54083,54091,54101,54121,54133,54139,54151,54163,54167,54181,54193,54217,54251,54269,54277,54287,54293,54311,54319,54323,54331,54347,54361,54367,54371,54377,54401,54403,54409,54413,54419,54421,54437,54443,54449,54469,54493,54497,54499,54503,54517,54521,54539,54541,54547,54559,54563,54577,54581,54583,54601,54617,54623,54629,54631,54647,54667,54673,54679,54709,54713,54721,54727,54751,54767,54773,54779,54787,54799,54829,54833,54851,54869,54877,54881,54907,54917,54919,54941,54949,54959,54973,54979,54983,55001,55009,55021,55049,55051,55057,55061,55073,55079,55103,55109,55117,55127,55147,55163,55171,55201,55207,55213,55217,55219,55229,55243,55249,55259,55291,55313,55331,55333,55337,55339,55343,55351,55373,55381,55399,55411,55439,55441,55457,55469,55487,55501,55511,55529,55541,55547,55579,55589,55603,55609,55619,55621,55631,55633,55639,55661,55663,55667,55673,55681,55691,55697,55711,55717,55721,55733,55763,55787,55793,55799,55807,55813,55817,55819,55823,55829,55837,55843,55849,55871,55889,55897,55901,55903,55921,55927,55931,55933,55949,55967,55987,55997,56003,56009,56039,56041,56053,56081,56087,56093,56099,56101,56113,56123,56131,56149,56167,56171,56179,56197,56207,56209,56237,56239,56249,56263,56267,56269,56299,56311,56333,56359,56369,56377,56383,56393,56401,56417,56431,56437,56443,56453,56467,56473,56477,56479,56489,56501,56503,56509,56519,56527,56531,56533,56543,56569,56591,56597,56599,56611,56629,56633,56659,56663,56671,56681,56687,56701,56711,56713,56731,56737,56747,56767,56773,56779,56783,56807,56809,56813,56821,56827,56843,56857,56873,56891,56893,56897,56909,56911,56921,56923,56929,56941,56951,56957,56963,56983,56989,56993,56999,57037,57041,57047,57059,57073,57077,57089,57097,57107,57119,57131,57139,57143,57149,57163,57173,57179,57191,57193,57203,57221,57223,57241,57251,57259,57269,57271,57283,57287,57301,57329,57331,57347,57349,57367,57373,57383,57389,57397,57413,57427,57457,57467,57487,57493,57503,57527,57529,57557,57559,57571,57587,57593,57601,57637,57641,57649,57653,57667,57679,57689,57697,57709,57713,57719,57727,57731,57737,57751,57773,57781,57787,57791,57793,57803,57809,57829,57839,57847,57853,57859,57881,57899,57901,57917,57923,57943,57947,57973,57977,57991,58013,58027,58031,58043,58049,58057,58061,58067,58073,58099,58109,58111,58129,58147,58151,58153,58169,58171,58189,58193,58199,58207,58211,58217,58229,58231,58237,58243,58271,58309,58313,58321,58337,58363,58367,58369,58379,58391,58393,58403,58411,58417,58427,58439,58441,58451,58453,58477,58481,58511,58537,58543,58549,58567,58573,58579,58601,58603,58613,58631,58657,58661,58679,58687,58693,58699,58711,58727,58733,58741,58757,58763,58771,58787,58789,58831,58889,58897,58901,58907,58909,58913,58921,58937,58943,58963,58967,58979,58991,58997,59009,59011,59021,59023,59029,59051,59053,59063,59069,59077,59083,59093,59107,59113,59119,59123,59141,59149,59159,59167,59183,59197,59207,59209,59219,59221,59233,59239,59243,59263,59273,59281,59333,59341,59351,59357,59359,59369,59377,59387,59393,59399,59407,59417,59419,59441,59443,59447,59453,59467,59471,59473,59497,59509,59513,59539,59557,59561,59567,59581,59611,59617,59621,59627,59629,59651,59659,59663,59669,59671,59693,59699,59707,59723,59729,59743,59747,59753,59771,59779,59791,59797,59809,59833,59863,59879,59887,59921,59929,59951,59957,59971,59981,59999,60013,60017,60029,60037,60041,60077,60083,60089,60091,60101,60103,60107,60127,60133,60139,60149,60161,60167,60169,60209,60217,60223,60251,60257,60259,60271,60289,60293,60317,60331,60337,60343,60353,60373,60383,60397,60413,60427,60443,60449,60457,60493,60497,60509,60521,60527,60539,60589,60601,60607,60611,60617,60623,60631,60637,60647,60649,60659,60661,60679,60689,60703,60719,60727,60733,60737,60757,60761,60763,60773,60779,60793,60811,60821,60859,60869,60887,60889,60899,60901,60913,60917,60919,60923,60937,60943,60953,60961,61001,61007,61027,61031,61043,61051,61057,61091,61099,61121,61129,61141,61151,61153,61169,61211,61223,61231,61253,61261,61283,61291,61297,61331,61333,61339,61343,61357,61363,61379,61381,61403,61409,61417,61441,61463,61469,61471,61483,61487,61493,61507,61511,61519,61543,61547,61553,61559,61561,61583,61603,61609,61613,61627,61631,61637,61643,61651,61657,61667,61673,61681,61687,61703,61717,61723,61729,61751,61757,61781,61813,61819,61837,61843,61861,61871,61879,61909,61927,61933,61949,61961,61967,61979,61981,61987,61991,62003,62011,62017,62039,62047,62053,62057,62071,62081,62099,62119,62129,62131,62137,62141,62143,62171,62189,62191,62201,62207,62213,62219,62233,62273,62297,62299,62303,62311,62323,62327,62347,62351,62383,62401,62417,62423,62459,62467,62473,62477,62483,62497,62501,62507,62533,62539,62549,62563,62581,62591,62597,62603,62617,62627,62633,62639,62653,62659,62683,62687,62701,62723,62731,62743,62753,62761,62773,62791,62801,62819,62827,62851,62861,62869,62873,62897,62903,62921,62927,62929,62939,62969,62971,62981,62983,62987,62989,63029,63031,63059,63067,63073,63079,63097,63103,63113,63127,63131,63149,63179,63197,63199,63211,63241,63247,63277,63281,63299,63311,63313,63317,63331,63337,63347,63353,63361,63367,63377,63389,63391,63397,63409,63419,63421,63439,63443,63463,63467,63473,63487,63493,63499,63521,63527,63533,63541,63559,63577,63587,63589,63599,63601,63607,63611,63617,63629,63647,63649,63659,63667,63671,63689,63691,63697,63703,63709,63719,63727,63737,63743,63761,63773,63781,63793,63799,63803,63809,63823,63839,63841,63853,63857,63863,63901,63907,63913,63929,63949,63977,63997,64007,64013,64019,64033,64037,64063,64067,64081,64091,64109,64123,64151,64153,64157,64171,64187,64189,64217,64223,64231,64237,64271,64279,64283,64301,64303,64319,64327,64333,64373,64381,64399,64403,64433,64439,64451,64453,64483,64489,64499,64513,64553,64567,64577,64579,64591,64601,64609,64613,64621,64627,64633,64661,64663,64667,64679,64693,64709,64717,64747,64763,64781,64783,64793,64811,64817,64849,64853,64871,64877,64879,64891,64901,64919,64921,64927,64937,64951,64969,64997,65003,65011,65027,65029,65033,65053,65063,65071,65089,65099,65101,65111,65119,65123,65129,65141,65147,65167,65171,65173,65179,65183,65203,65213,65239,65257,65267,65269,65287,65293,65309,65323,65327,65353,65357,65371,65381,65393,65407,65413,65419,65423,65437,65447,65449,65479,65497,65519,65521,65537,65539,65543,65551,65557,65563,65579,65581,65587,65599,65609,65617,65629,65633,65647,65651,65657,65677,65687,65699,65701,65707,65713,65717,65719,65729,65731,65761,65777,65789,65809,65827,65831,65837,65839,65843,65851,65867,65881,65899,65921,65927,65929,65951,65957,65963,65981,65983,65993,66029,66037,66041,66047,66067,66071,66083,66089,66103,66107,66109,66137,66161,66169,66173,66179,66191,66221,66239,66271,66293,66301,66337,66343,66347,66359,66361,66373,66377,66383,66403,66413,66431,66449,66457,66463,66467,66491,66499,66509,66523,66529,66533,66541,66553,66569,66571,66587,66593,66601,66617,66629,66643,66653,66683,66697,66701,66713,66721,66733,66739,66749,66751,66763,66791,66797,66809,66821,66841,66851,66853,66863,66877,66883,66889,66919,66923,66931,66943,66947,66949,66959,66973,66977,67003,67021,67033,67043,67049,67057,67061,67073,67079,67103,67121,67129,67139,67141,67153,67157,67169,67181,67187,67189,67211,67213,67217,67219,67231,67247,67261,67271,67273,67289,67307,67339,67343,67349,67369,67391,67399,67409,67411,67421,67427,67429,67433,67447,67453,67477,67481,67489,67493,67499,67511,67523,67531,67537,67547,67559,67567,67577,67579,67589,67601,67607,67619,67631,67651,67679,67699,67709,67723,67733,67741,67751,67757,67759,67763,67777,67783,67789,67801,67807,67819,67829,67843,67853,67867,67883,67891,67901,67927,67931,67933,67939,67943,67957,67961,67967,67979,67987,67993,68023,68041,68053,68059,68071,68087,68099,68111,68113,68141,68147,68161,68171,68207,68209,68213,68219,68227,68239,68261,68279,68281,68311,68329,68351,68371,68389,68399,68437,68443,68447,68449,68473,68477,68483,68489,68491,68501,68507,68521,68531,68539,68543,68567,68581,68597,68611,68633,68639,68659,68669,68683,68687,68699,68711,68713,68729,68737,68743,68749,68767,68771,68777,68791,68813,68819,68821,68863,68879,68881,68891,68897,68899,68903,68909,68917,68927,68947,68963,68993,69001,69011,69019,69029,69031,69061,69067,69073,69109,69119,69127,69143,69149,69151,69163,69191,69193,69197,69203,69221,69233,69239,69247,69257,69259,69263,69313,69317,69337,69341,69371,69379,69383,69389,69401,69403,69427,69431,69439,69457,69463,69467,69473,69481,69491,69493,69497,69499,69539,69557,69593,69623,69653,69661,69677,69691,69697,69709,69737,69739,69761,69763,69767,69779,69809,69821,69827,69829,69833,69847,69857,69859,69877,69899,69911,69929,69931,69941,69959,69991,69997,70001,70003,70009,70019,70039,70051,70061,70067,70079,70099,70111,70117,70121,70123,70139,70141,70157,70163,70177,70181,70183,70199,70201,70207,70223,70229,70237,70241,70249,70271,70289,70297,70309,70313,70321,70327,70351,70373,70379,70381,70393,70423,70429,70439,70451,70457,70459,70481,70487,70489,70501,70507,70529,70537,70549,70571,70573,70583,70589,70607,70619,70621,70627,70639,70657,70663,70667,70687,70709,70717,70729,70753,70769,70783,70793,70823,70841,70843,70849,70853,70867,70877,70879,70891,70901,70913,70919,70921,70937,70949,70951,70957,70969,70979,70981,70991,70997,70999,71011,71023,71039,71059,71069,71081,71089,71119,71129,71143,71147,71153,71161,71167,71171,71191,71209,71233,71237,71249,71257,71261,71263,71287,71293,71317,71327,71329,71333,71339,71341,71347,71353,71359,71363,71387,71389,71399,71411,71413,71419,71429,71437,71443,71453,71471,71473,71479,71483,71503,71527,71537,71549,71551,71563,71569,71593,71597,71633,71647,71663,71671,71693,71699,71707,71711,71713,71719,71741,71761,71777,71789,71807,71809,71821,71837,71843,71849,71861,71867,71879,71881,71887,71899,71909,71917,71933,71941,71947,71963,71971,71983,71987,71993,71999,72019,72031,72043,72047,72053,72073,72077,72089,72091,72101,72103,72109,72139,72161,72167,72169,72173,72211,72221,72223,72227,72229,72251,72253,72269,72271,72277,72287,72307,72313,72337,72341,72353,72367,72379,72383,72421,72431,72461,72467,72469,72481,72493,72497,72503,72533,72547,72551,72559,72577,72613,72617,72623,72643,72647,72649,72661,72671,72673,72679,72689,72701,72707,72719,72727,72733,72739,72763,72767,72797,72817,72823,72859,72869,72871,72883,72889,72893,72901,72907,72911,72923,72931,72937,72949,72953,72959,72973,72977,72997,73009,73013,73019,73037,73039,73043,73061,73063,73079,73091,73121,73127,73133,73141,73181,73189,73237,73243,73259,73277,73291,73303,73309,73327,73331,73351,73361,73363,73369,73379,73387,73417,73421,73433,73453,73459,73471,73477,73483,73517,73523,73529,73547,73553,73561,73571,73583,73589,73597,73607,73609,73613,73637,73643,73651,73673,73679,73681,73693,73699,73709,73721,73727,73751,73757,73771,73783,73819,73823,73847,73849,73859,73867,73877,73883,73897,73907,73939,73943,73951,73961,73973,73999,74017,74021,74027,74047,74051,74071,74077,74093,74099,74101,74131,74143,74149,74159,74161,74167,74177,74189,74197,74201,74203,74209,74219,74231,74257,74279,74287,74293,74297,74311,74317,74323,74353,74357,74363,74377,74381,74383,74411,74413,74419,74441,74449,74453,74471,74489,74507,74509,74521,74527,74531,74551,74561,74567,74573,74587,74597,74609,74611,74623,74653,74687,74699,74707,74713,74717,74719,74729,74731,74747,74759,74761,74771,74779,74797,74821,74827,74831,74843,74857,74861,74869,74873,74887,74891,74897,74903,74923,74929,74933,74941,74959,75011,75013,75017,75029,75037,75041,75079,75083,75109,75133,75149,75161,75167,75169,75181,75193,75209,75211,75217,75223,75227,75239,75253,75269,75277,75289,75307,75323,75329,75337,75347,75353,75367,75377,75389,75391,75401,75403,75407,75431,75437,75479,75503,75511,75521,75527,75533,75539,75541,75553,75557,75571,75577,75583,75611,75617,75619,75629,75641,75653,75659,75679,75683,75689,75703,75707,75709,75721,75731,75743,75767,75773,75781,75787,75793,75797,75821,75833,75853,75869,75883,75913,75931,75937,75941,75967,75979,75983,75989,75991,75997,76001,76003,76031,76039,76079,76081,76091,76099,76103,76123,76129,76147,76157,76159,76163,76207,76213,76231,76243,76249,76253,76259,76261,76283,76289,76303,76333,76343,76367,76369,76379,76387,76403,76421,76423,76441,76463,76471,76481,76487,76493,76507,76511,76519,76537,76541,76543,76561,76579,76597,76603,76607,76631,76649,76651,76667,76673,76679,76697,76717,76733,76753,76757,76771,76777,76781,76801,76819,76829,76831,76837,76847,76871,76873,76883,76907,76913,76919,76943,76949,76961,76963,76991,77003,77017,77023,77029,77041,77047,77069,77081,77093,77101,77137,77141,77153,77167,77171,77191,77201,77213,77237,77239,77243,77249,77261,77263,77267,77269,77279,77291,77317,77323,77339,77347,77351,77359,77369,77377,77383,77417,77419,77431,77447,77471,77477,77479,77489,77491,77509,77513,77521,77527,77543,77549,77551,77557,77563,77569,77573,77587,77591,77611,77617,77621,77641,77647,77659,77681,77687,77689,77699,77711,77713,77719,77723,77731,77743,77747,77761,77773,77783,77797,77801,77813,77839,77849,77863,77867,77893,77899,77929,77933,77951,77969,77977,77983,77999,78007,78017,78031,78041,78049,78059,78079,78101,78121,78137,78139,78157,78163,78167,78173,78179,78191,78193,78203,78229,78233,78241,78259,78277,78283,78301,78307,78311,78317,78341,78347,78367,78401,78427,78437,78439,78467,78479,78487,78497,78509,78511,78517,78539,78541,78553,78569,78571,78577,78583,78593,78607,78623,78643,78649,78653,78691,78697,78707,78713,78721,78737,78779,78781,78787,78791,78797,78803,78809,78823,78839,78853,78857,78877,78887,78889,78893,78901,78919,78929,78941,78977,78979,78989,79031,79039,79043,79063,79087,79103,79111,79133,79139,79147,79151,79153,79159,79181,79187,79193,79201,79229,79231,79241,79259,79273,79279,79283,79301,79309,79319,79333,79337,79349,79357,79367,79379,79393,79397,79399,79411,79423,79427,79433,79451,79481,79493,79531,79537,79549,79559,79561,79579,79589,79601,79609,79613,79621,79627,79631,79633,79657,79669,79687,79691,79693,79697,79699,79757,79769,79777,79801,79811,79813,79817,79823,79829,79841,79843,79847,79861,79867,79873,79889,79901,79903,79907,79939,79943,79967,79973,79979,79987,79997,79999,80021,80039,80051,80071,80077,80107,80111,80141,80147,80149,80153,80167,80173,80177,80191,80207,80209,80221,80231,80233,80239,80251,80263,80273,80279,80287,80309,80317,80329,80341,80347,80363,80369,80387,80407,80429,80447,80449,80471,80473,80489,80491,80513,80527,80537,80557,80567,80599,80603,80611,80621,80627,80629,80651,80657,80669,80671,80677,80681,80683,80687,80701,80713,80737,80747,80749,80761,80777,80779,80783,80789,80803,80809,80819,80831,80833,80849,80863,80897,80909,80911,80917,80923,80929,80933,80953,80963,80989,81001,81013,81017,81019,81023,81031,81041,81043,81047,81049,81071,81077,81083,81097,81101,81119,81131,81157,81163,81173,81181,81197,81199,81203,81223,81233,81239,81281,81283,81293,81299,81307,81331,81343,81349,81353,81359,81371,81373,81401,81409,81421,81439,81457,81463,81509,81517,81527,81533,81547,81551,81553,81559,81563,81569,81611,81619,81629,81637,81647,81649,81667,81671,81677,81689,81701,81703,81707,81727,81737,81749,81761,81769,81773,81799,81817,81839,81847,81853,81869,81883,81899,81901,81919,81929,81931,81937,81943,81953,81967,81971,81973,82003,82007,82009,82013,82021,82031,82037,82039,82051,82067,82073,82129,82139,82141,82153,82163,82171,82183,82189,82193,82207,82217,82219,82223,82231,82237,82241,82261,82267,82279,82301,82307,82339,82349,82351,82361,82373,82387,82393,82421,82457,82463,82469,82471,82483,82487,82493,82499,82507,82529,82531,82549,82559,82561,82567,82571,82591,82601,82609,82613,82619,82633,82651,82657,82699,82721,82723,82727,82729,82757,82759,82763,82781,82787,82793,82799,82811,82813,82837,82847,82883,82889,82891,82903,82913,82939,82963,82981,82997,83003,83009,83023,83047,83059,83063,83071,83077,83089,83093,83101,83117,83137,83177,83203,83207,83219,83221,83227,83231,83233,83243,83257,83267,83269,83273,83299,83311,83339,83341,83357,83383,83389,83399,83401,83407,83417,83423,83431,83437,83443,83449,83459,83471,83477,83497,83537,83557,83561,83563,83579,83591,83597,83609,83617,83621,83639,83641,83653,83663,83689,83701,83717,83719,83737,83761,83773,83777,83791,83813,83833,83843,83857,83869,83873,83891,83903,83911,83921,83933,83939,83969,83983,83987,84011,84017,84047,84053,84059,84061,84067,84089,84121,84127,84131,84137,84143,84163,84179,84181,84191,84199,84211,84221,84223,84229,84239,84247,84263,84299,84307,84313,84317,84319,84347,84349,84377,84389,84391,84401,84407,84421,84431,84437,84443,84449,84457,84463,84467,84481,84499,84503,84509,84521,84523,84533,84551,84559,84589,84629,84631,84649,84653,84659,84673,84691,84697,84701,84713,84719,84731,84737,84751,84761,84787,84793,84809,84811,84827,84857,84859,84869,84871,84913,84919,84947,84961,84967,84977,84979,84991,85009,85021,85027,85037,85049,85061,85081,85087,85091,85093,85103,85109,85121,85133,85147,85159,85193,85199,85201,85213,85223,85229,85237,85243,85247,85259,85297,85303,85313,85331,85333,85361,85363,85369,85381,85411,85427,85429,85439,85447,85451,85453,85469,85487,85513,85517,85523,85531,85549,85571,85577,85597,85601,85607,85619,85621,85627,85639,85643,85661,85667,85669,85691,85703,85711,85717,85733,85751,85781,85793,85817,85819,85829,85831,85837,85843,85847,85853,85889,85903,85909,85931,85933,85991,85999,86011,86017,86027,86029,86069,86077,86083,86111,86113,86117,86131,86137,86143,86161,86171,86179,86183,86197,86201,86209,86239,86243,86249,86257,86263,86269,86287,86291,86293,86297,86311,86323,86341,86351,86353,86357,86369,86371,86381,86389,86399,86413,86423,86441,86453,86461,86467,86477,86491,86501,86509,86531,86533,86539,86561,86573,86579,86587,86599,86627,86629,86677,86689,86693,86711,86719,86729,86743,86753,86767,86771,86783,86813,86837,86843,86851,86857,86861,86869,86923,86927,86929,86939,86951,86959,86969,86981,86993,87011,87013,87037,87041,87049,87071,87083,87103,87107,87119,87121,87133,87149,87151,87179,87181,87187,87211,87221,87223,87251,87253,87257,87277,87281,87293,87299,87313,87317,87323,87337,87359,87383,87403,87407,87421,87427,87433,87443,87473,87481,87491,87509,87511,87517,87523,87539,87541,87547,87553,87557,87559,87583,87587,87589,87613,87623,87629,87631,87641,87643,87649,87671,87679,87683,87691,87697,87701,87719,87721,87739,87743,87751,87767,87793,87797,87803,87811,87833,87853,87869,87877,87881,87887,87911,87917,87931,87943,87959,87961,87973,87977,87991,88001,88003,88007,88019,88037,88069,88079,88093,88117,88129,88169,88177,88211,88223,88237,88241,88259,88261,88289,88301,88321,88327,88337,88339,88379,88397,88411,88423,88427,88463,88469,88471,88493,88499,88513,88523,88547,88589,88591,88607,88609,88643,88651,88657,88661,88663,88667,88681,88721,88729,88741,88747,88771,88789,88793,88799,88801,88807,88811,88813,88817,88819,88843,88853,88861,88867,88873,88883,88897,88903,88919,88937,88951,88969,88993,88997,89003,89009,89017,89021,89041,89051,89057,89069,89071,89083,89087,89101,89107,89113,89119,89123,89137,89153,89189,89203,89209,89213,89227,89231,89237,89261,89269,89273,89293,89303,89317,89329,89363,89371,89381,89387,89393,89399,89413,89417,89431,89443,89449,89459,89477,89491,89501,89513,89519,89521,89527,89533,89561,89563,89567,89591,89597,89599,89603,89611,89627,89633,89653,89657,89659,89669,89671,89681,89689,89753,89759,89767,89779,89783,89797,89809,89819,89821,89833,89839,89849,89867,89891,89897,89899,89909,89917,89923,89939,89959,89963,89977,89983,89989,90001,90007,90011,90017,90019,90023,90031,90053,90059,90067,90071,90073,90089,90107,90121,90127,90149,90163,90173,90187,90191,90197,90199,90203,90217,90227,90239,90247,90263,90271,90281,90289,90313,90353,90359,90371,90373,90379,90397,90401,90403,90407,90437,90439,90469,90473,90481,90499,90511,90523,90527,90529,90533,90547,90583,90599,90617,90619,90631,90641,90647,90659,90677,90679,90697,90703,90709,90731,90749,90787,90793,90803,90821,90823,90833,90841,90847,90863,90887,90901,90907,90911,90917,90931,90947,90971,90977,90989,90997,91009,91019,91033,91079,91081,91097,91099,91121,91127,91129,91139,91141,91151,91153,91159,91163,91183,91193,91199,91229,91237,91243,91249,91253,91283,91291,91297,91303,91309,91331,91367,91369,91373,91381,91387,91393,91397,91411,91423,91433,91453,91457,91459,91463,91493,91499,91513,91529,91541,91571,91573,91577,91583,91591,91621,91631,91639,91673,91691,91703,91711,91733,91753,91757,91771,91781,91801,91807,91811,91813,91823,91837,91841,91867,91873,91909,91921,91939,91943,91951,91957,91961,91967,91969,91997,92003,92009,92033,92041,92051,92077,92083,92107,92111,92119,92143,92153,92173,92177,92179,92189,92203,92219,92221,92227,92233,92237,92243,92251,92269,92297,92311,92317,92333,92347,92353,92357,92363,92369,92377,92381,92383,92387,92399,92401,92413,92419,92431,92459,92461,92467,92479,92489,92503,92507,92551,92557,92567,92569,92581,92593,92623,92627,92639,92641,92647,92657,92669,92671,92681,92683,92693,92699,92707,92717,92723,92737,92753,92761,92767,92779,92789,92791,92801,92809,92821,92831,92849,92857,92861,92863,92867,92893,92899,92921,92927,92941,92951,92957,92959,92987,92993,93001,93047,93053,93059,93077,93083,93089,93097,93103,93113,93131,93133,93139,93151,93169,93179,93187,93199,93229,93239,93241,93251,93253,93257,93263,93281,93283,93287,93307,93319,93323,93329,93337,93371,93377,93383,93407,93419,93427,93463,93479,93481,93487,93491,93493,93497,93503,93523,93529,93553,93557,93559,93563,93581,93601,93607,93629,93637,93683,93701,93703,93719,93739,93761,93763,93787,93809,93811,93827,93851,93871,93887,93889,93893,93901,93911,93913,93923,93937,93941,93949,93967,93971,93979,93983,93997,94007,94009,94033,94049,94057,94063,94079,94099,94109,94111,94117,94121,94151,94153,94169,94201,94207,94219,94229,94253,94261,94273,94291,94307,94309,94321,94327,94331,94343,94349,94351,94379,94397,94399,94421,94427,94433,94439,94441,94447,94463,94477,94483,94513,94529,94531,94541,94543,94547,94559,94561,94573,94583,94597,94603,94613,94621,94649,94651,94687,94693,94709,94723,94727,94747,94771,94777,94781,94789,94793,94811,94819,94823,94837,94841,94847,94849,94873,94889,94903,94907,94933,94949,94951,94961,94993,94999,95003,95009,95021,95027,95063,95071,95083,95087,95089,95093,95101,95107,95111,95131,95143,95153,95177,95189,95191,95203,95213,95219,95231,95233,95239,95257,95261,95267,95273,95279,95287,95311,95317,95327,95339,95369,95383,95393,95401,95413,95419,95429,95441,95443,95461,95467,95471,95479,95483,95507,95527,95531,95539,95549,95561,95569,95581,95597,95603,95617,95621,95629,95633,95651,95701,95707,95713,95717,95723,95731,95737,95747,95773,95783,95789,95791,95801,95803,95813,95819,95857,95869,95873,95881,95891,95911,95917,95923,95929,95947,95957,95959,95971,95987,95989,96001,96013,96017,96043,96053,96059,96079,96097,96137,96149,96157,96167,96179,96181,96199,96211,96221,96223,96233,96259,96263,96269,96281,96289,96293,96323,96329,96331,96337,96353,96377,96401,96419,96431,96443,96451,96457,96461,96469,96479,96487,96493,96497,96517,96527,96553,96557,96581,96587,96589,96601,96643,96661,96667,96671,96697,96703,96731,96737,96739,96749,96757,96763,96769,96779,96787,96797,96799,96821,96823,96827,96847,96851,96857,96893,96907,96911,96931,96953,96959,96973,96979,96989,96997,97001,97003,97007,97021,97039,97073,97081,97103,97117,97127,97151,97157,97159,97169,97171,97177,97187,97213,97231,97241,97259,97283,97301,97303,97327,97367,97369,97373,97379,97381,97387,97397,97423,97429,97441,97453,97459,97463,97499,97501,97511,97523,97547,97549,97553,97561,97571,97577,97579,97583,97607,97609,97613,97649,97651,97673,97687,97711,97729,97771,97777,97787,97789,97813,97829,97841,97843,97847,97849,97859,97861,97871,97879,97883,97919,97927,97931,97943,97961,97967,97973,97987,98009,98011,98017,98041,98047,98057,98081,98101,98123,98129,98143,98179,98207,98213,98221,98227,98251,98257,98269,98297,98299,98317,98321,98323,98327,98347,98369,98377,98387,98389,98407,98411,98419,98429,98443,98453,98459,98467,98473,98479,98491,98507,98519,98533,98543,98561,98563,98573,98597,98621,98627,98639,98641,98663,98669,98689,98711,98713,98717,98729,98731,98737,98773,98779,98801,98807,98809,98837,98849,98867,98869,98873,98887,98893,98897,98899,98909,98911,98927,98929,98939,98947,98953,98963,98981,98993,98999,99013,99017,99023,99041,99053,99079,99083,99089,99103,99109,99119,99131,99133,99137,99139,99149,99173,99181,99191,99223,99233,99241,99251,99257,99259,99277,99289,99317,99347,99349,99367,99371,99377,99391,99397,99401,99409,99431,99439,99469,99487,99497,99523,99527,99529,99551,99559,99563,99571,99577,99581,99607,99611,99623,99643,99661,99667,99679,99689,99707,99709,99713,99719,99721,99733,99761,99767,99787,99793,99809,99817,99823,99829,99833,99839,99859,99871,99877,99881,99901,99907,99923,99929,99961,99971,99989,99991}; 7 const int maxn=55; 8 int n,a[55][maxn],A[maxn],cnt; 9 int dfs(int dep) 10 { 11 if(A[n]<=1) 12 { 13 int ans=0; 14 for(int i=n;i&&A[i];i--)ans+=A[i]; 15 return ans; 16 } 17 int res=0x7fffffff; 18 memcpy(a[dep],A,sizeof(A)); 19 for(int i=0;prime[i]<=a[dep][n]&&i<=9591;i++) 20 { 21 int tmp=0; 22 for(int j=1;j<=n;j++)tmp+=A[j]%prime[i],A[j]/=prime[i]; 23 if(tmp<res)res=min(res,dfs(dep+1)+tmp); 24 memcpy(A,a[dep],sizeof(A)); 25 } 26 return res; 27 } 28 int haha() 29 { 30 scanf("%d",&n); 31 if(n==1) 32 { 33 cout<<1; 34 return 0; 35 } 36 for(int i=1;i<=n;i++)scanf("%d",&A[i]); 37 sort(A+1,A+n+1); 38 printf("%d\\n",dfs(0)); 39 } 40 int sb=haha(); 41 int main(){;}
Fiolki
给出建边顺序和连通后点合并顺序，问最后合并得到的最大权值。
这个思路只对于我来说是个新思路：重构树。把这个点往上一推，跟另一个点直接合并，然后根据$LCA$层数为第一关键字反应顺序第二关键字进行排序处理。
1 #include<iostream> 2 #include<cstdio> 3 #include<algorithm> 4 #include<cstring> 5 using namespace std; 6 const int maxn=500010; 7 struct node 8 { 9 int from,to,next; 10 }edge[maxn<<1]; 11 int head[maxn],tot=0,cnt=0; 12 void addedge(int u,int v) 13 { 14 edge[++tot]=(node){u,v,head[u]};head[u]=tot; 15 } 16 int dep[maxn],rt[maxn][25],tim,dfn[maxn]; 17 void dfs(int root,int fa,int deep,int timm) 18 { 19 rt[root][0]=fa;dep[root]=deep;dfn[root]=timm; 20 for(int i=1;i<=20;i++) 21 if((1<<i)<dep[root])rt[root][i]=rt[rt[root][i-1]][i-1]; 22 else break; 23 for(int i=head[root];i;i=edge[i].next) 24 { 25 int v=edge[i].to; 26 if(!rt[v][0])dfs(v,root,deep+1,timm); 27 } 28 } 29 int n,m,k; 30 int lca(int x,int y) 31 { 32 int i; 33 if(dep[x]<dep[y])swap(x,y); 34 for(i=0;(1<<i)<=dep[x];i++);i--; 35 for(int j=i;j>=0;j--) 36 if(dep[x]-(1<<j)>=dep[y])x=rt[x][j]; 37 if(x==y)return x; 38 for(int j=i;j>=0;j--) 39 if(rt[x][j]!=-1&&rt[x][j]!=rt[y][j])x=rt[x][j],y=rt[y][j]; 40 return rt[x][0]; 41 } 42 struct ques 43 { 44 int x,y,dep,id; 45 bool operator <(const ques &b)const 46 { 47 if(dep!=b.dep)return dep>b.dep; 48 return id<b.id; 49 } 50 }question[maxn]; 51 int g[maxn],id[maxn]; 52 int haha() 53 { 54 scanf("%d%d%d",&n,&m,&k); 55 for(int i=1;i<=n;i++)id[i]=i,scanf("%d",&g[i]); 56 for(int i=1;i<=m;i++) 57 { 58 int x,y;scanf("%d%d",&x,&y); 59 addedge(n+i,id[x]);addedge(id[x],n+i);addedge(n+i,id[y]);addedge(id[y],n+i);id[y]=n+i; 60 } 61 for(int i=n+m;i;i--)if(!rt[i][0])dfs(i,-1,1,++tim); 62 for(int i=1;i<=k;i++) 63 { 64 int x,y;scanf("%d%d",&x,&y); 65 if(dfn[x]==dfn[y])question[++cnt]=(ques){x,y,dep[lca(x,y)],i}; 66 } 67 sort(question+1,question+cnt+1); 68 long long ans=0; 69 for(int i=1;i<=cnt;i++) 70 { 71 int x=question[i].x,y=question[i].y;long long delta=min(g[x],g[y]); 72 ans+=1ll*delta,g[x]-=delta,g[y]-=delta; 73 } 74 printf("%lld\\n",1ll*ans<<1); 75 //while(1); 76 } 77 int sb=haha(); 78 int main(){;}
大逃亡
找出距离平面上多个固定点最小值最远的一条路。
正解是二分答案加$bfs$验证……然而我想了一个奇葩思路……$bfs$一遍之后对整个矩阵重新建边……然后二分答案的基础上每次只用大于这个距离的边跑$SPFA$……（考试时建边次数过多爆零……）
1 #include<iostream> 2 #include<cstdio> 3 #include<algorithm> 4 #include<cstring> 5 #include<queue> 6 using namespace std; 7 const int maxn=10005,maxx=1005; 8 queue<int>qx,qy; 9 struct node 10 { 11 int from,to,dis,next; 12 }edge[maxx*maxx<<3]; 13 int head[maxx*maxx],tot; 14 void addedge(int u,int v,int w) 15 { 16 edge[++tot]=(node){u,v,w,head[u]};head[u]=tot; 17 } 18 int dis[maxx][maxx],dist[maxx*maxx],x[maxn],y[maxn],n,sx,sy,ex,ey,X,Y,dx[4]={0,0,1,-1},dy[4]={1,-1,0,0},id[maxx][maxx],longest; 19 void bfs() 20 { 21 while(!qx.empty()) 22 { 23 int tx=qx.front(),ty=qy.front(); 24 qx.pop();qy.pop(); 25 for(int d=0;d<4;d++) 26 { 27 int tmpx=tx+dx[d],tmpy=ty+dy[d]; 28 if(tmpx<0||tmpx>=X||tmpy<0||tmpy>=Y)continue; 29 if(dis[tx][ty]==-1||dis[tmpx][tmpy]==-1)addedge(id[tx][ty],id[tmpx][tmpy],0),addedge(id[tmpx][tmpy],id[tx][ty],0); 30 else addedge(id[tmpx][tmpy],id[tx][ty],(dis[tmpx][tmpy]==0?dis[tx][ty]:min(dis[tmpx][tmpy],dis[tx][ty]))),addedge(id[tx][ty],id[tmpx][tmpy],(dis[tmpx][tmpy]==0?dis[tx][ty]:min(dis[tx][ty],dis[tmpx][tmpy]))); 31 if(dis[tmpx][tmpy]!=0)continue; 32 dis[tmpx][tmpy]=(dis[tx][ty]<0?1:dis[tx][ty]+1); 33 qx.push(tmpx);qy.push(tmpy);longest=max(longest,dis[tmpx][tmpy]); 34 } 35 } 36 } 37 int Q[65540]; 38 unsigned short h,t; 39 bool inqueue[maxx*maxx]; 40 bool spfa(int val) 41 { 42 for(int i=1;i<=X*Y;i++)dist[i]=0x7f7f7f7f/2;h=0,t=0; 43 dist[id[sx][sy]]=0;Q[t++]=id[sx][sy];inqueue[id[sx][sy]]=1; 44 while(h!=t) 45 { 46 int x=Q[h++];inqueue[x]=0; 47 for(int i=head[x];i;i=edge[i].next) 48 { 49 int v=edge[i].to; 50 if(edge[i].dis>=val&&dist[x]+1<dist[v]) 51 { 52 dist[v]=dist[x]+1; 53 if(!inqueue[v])inqueue[v]=1,Q[t++]=v; 54 } 55 } 56 } 57 return dist[id[ex][ey]]<0x7f7f7f7f/2; 58 } 59 bool visit[maxx][maxx]; 60 bool check(int val) 61 { 62 return spfa(val); 63 } 64 int haha() 65 { 66 scanf("%d%d%d",&n,&X,&Y);scanf("%d%d%d%d",&sx,&sy,&ex,&ey); 67 for(int i=1;i<=n;i++) 68 { 69 scanf("%d%d",&x[i],&y[i]); 70 dis[x[i]][y[i]]=-1; 71 qx.push(x[i]);qy.push(y[i]); 72 } 73 int cnt=0; 74 for(int i=0;i<X;i++) 75 for(int j=0;j<Y;j++)id[i][j]=++cnt; 76 bfs(); 77 int l=0,r=longest,mid,ans=0,step; 78 spfa(0);step=dist[id[ex][ey]]; 79 while(l<=r) 80 { 81 mid=(l+r)>>1; 82 if(check(mid))l=mid+1,ans=mid,step=dist[id[ex][ey]]; 83 else r=mid-1; 84 } 85 printf("%d %d\\n",ans,step); 86 } 87 int sb=haha(); 88 int main(){;}
（即使不重新建边也是丧心病狂的用了循环队列才卡过的……）
通信
给出一张有向图，$SCC$中点传递不需要花费，找出信息传递最小花费。
傻乎乎的打了个克鲁斯卡尔……然后有向图……$GG$……结局是一个奥妙重重的贪心……
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int maxn=50005,maxm=100005; 7 struct node 8 { 9 int from,to,dis,next; 10 bool operator <(const node &b)const 11 { 12 return dis<b.dis; 13 } 14 }edge[maxm<<1]; 15 int head[maxn],tot,n,m; 16 void addedge(int u,int v,int w) 17 { 18 edge[++tot]=(node){u,v,w,head[u]};head[u]=tot; 19 } 20 int tim[maxn],ti,dfn[maxn],low[maxn],belong[maxn],cnt,scnt; 21 #include<stack> 22 stack<int>s; 23 void dfs(int now) 24 { 25 tim[now]=ti;low[now]=dfn[now]=++cnt;s.push(now); 26 for(int i=head[now];i;i=edge[i].next) 27 { 28 int v=edge[i].to; 29 if(tim[v]!=ti)dfs(v),low[now]=min(low[now],low[v]); 30 else if(!belong[v])low[now]=min(low[now],dfn[v]); 31 } 32 if(low[now]==dfn[now]) 33 { 34 scnt++;int k; 35 do 36 { 37 k=s.top();s.pop(); 38 belong[k]=scnt; 39 }while(k!=now); 40 } 41 } 42 int pa[maxn]; 43 int getfa(int x) 44 { 45 return pa[x]==x?x:pa[x]=getfa(pa[x]); 46 } 47 void unionn(int x,int y) 48 { 49 x=getfa(x),y=getfa(y); 50 if(x!=y)pa[y]=x; 51 } 52 int minn[maxn]; 53 int haha() 54 { 55 while(scanf("%d%d",&n,&m)!=EOF&&n) 56 { 57 ti++;tot=cnt=scnt=0;memset(belong,0,sizeof(belong));memset(head,0,sizeof(head)); 58 for(int i=1;i<=m;i++) 59 { 60 int x,y,z;scanf("%d%d%d",&x,&y,&z); 61 addedge(x,y,z); 62 } 63 for(int i=0;i<n;i++) 64 if(tim[i]!=ti)dfs(i); 65 memset(head,0,sizeof(head)); 66 for(int i=1;i<=m;i++) 67 { 68 int u=edge[i].from,v=edge[i].to; 69 if(belong[u]!=belong[v])addedge(belong[u],belong[v],edge[i].dis); 70 } 71 sort(edge+m+1,edge+tot+1); 72 int sum=0,num=0; 73 for(int i=1;i<=scnt;i++)pa[i]=i,minn[i]=2147483647; 74 for(int i=m+1;i<=tot;i++) 75 { 76 int v=edge[i].to; 77 minn[v]=min(minn[v],edge[i].dis); 78 } 79 int ans=0; 80 for(int i=1;i<=scnt;i++) 81 if(minn[i]!=2147483647)ans+=minn[i]; 82 printf("%d\\n",ans); 83 } 84 } 85 int sb=haha(); 86 int main(){;}
（可以看到我克鲁斯卡尔代码还在呢……）
奇袭
给出一个矩阵中敌军分布，求出有多少个子矩阵里面恰好有边长个敌军。保证每一行每一列只有一个敌军。
这一句话告诉我们歌者举起了二向箔实施了降维打击，变成了一个序列问题……然后神分治……
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 const int maxn=50005; 7 int pos[maxn],n,ans,minn[maxn],maxx[maxn],t[maxn*5]; 8 void solve(int l,int r) 9 { 10 if(l==r){ans++;return;}//分治终点，因为1*1一定合法直接自加 11 int mid=(l+r)>>1;minn[mid]=maxx[mid]=pos[mid];minn[mid+1]=maxx[mid+1]=pos[mid+1];//初始化，从中间向两端进行 12 int z1=mid+1,z2=mid+1;//初始化稍后使用的指针 13 for(int i=mid-1;i>=l;i--)minn[i]=min(minn[i+1],pos[i]),maxx[i]=max(maxx[i+1],pos[i]);//初始化从中间蔓延到左侧的最大值和最小值 14 for(int i=mid+2;i<=r;i++)minn[i]=min(minn[i-1],pos[i]),maxx[i]=max(maxx[i-1],pos[i]);//蔓延到右侧的最大值和最小值 15 for(int i=mid;i>=l;i--)//研究左侧的那一半 16 { 17 int j=maxx[i]-minn[i]+i;//计算出从中间到这里最大值和最小值差，再加上该点位置就是合法矩形右边界 18 if(j>mid&&j<=r&&maxx[j]<maxx[i]&&minn[j]>minn[i])ans++;//如果这个右边界合法（即：这个矩形跨过了中间值且没有超过右边界，并且这个矩形之中最大值和最小值就是左侧的最大值和最小值以保证合法），这个矩形就是合法的，方式数增加 19 while(z2<=r&&minn[z2]>=minn[i])t[maxx[z2]-z2+maxn]++,z2++;//如果最小值在左侧最大值在右侧，那么max(右半段)-min(左半段)=r-l，移项就可以得到max(右半段)-r=min(左半段)-l，反之亦然，如果max(右半段)-r=min(左半段)-l,那么这个区间就是合法的，这个对应的区间左端点数目增加 20 while(z1<=r&&maxx[z1]<=maxx[i])t[maxx[z1]-z1+maxn]--,z1++;//同理，寻找所有加入这个值之后不合法的右端点，踢掉 21 ans+=max(t[minn[i]-i+maxn],0);//统计答案 22 } 23 for(int i=l;i<=r;i++)t[maxx[i]-i+maxn]=0;z1=mid;z2=mid; 24 for(int i=mid+1;i<=r;i++) 25 { 26 int j=i-maxx[i]+minn[i]; 27 if(j<=mid&&j>=l&&maxx[j]<maxx[i]&&minn[j]>minn[i])ans++; 28 while(z2>=l&&minn[z2]>=minn[i])t[maxx[z2]+z2+maxn]++,z2--; 29 while(z1>=l&&maxx[z1]<=maxx[i])t[maxx[z1]+z1+maxn]--,z1--; 30 ans+=max(t[minn[i]+i+maxn],0); 31 } 32 for(int i=l;i<=r;i++)t[maxx[i]+i+maxn]=0; 33 solve(l,mid);solve(mid+1,r); 34 } 35 int haha() 36 { 37 scanf("%d",&n); 38 for(int i=1;i<=n;i++) 39 { 40 int x,y;scanf("%d%d",&x,&y); 41 pos[x]=y; 42 } 43 solve(1,n);printf("%d\\n",ans); 44 } 45 int sb=haha(); 46 int main(){;}
方程的解
求出线性方程的正整数解个数。
明眼人都知道怎么做……然而我口胡了一个解析几何……
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 using namespace std; 6 long long gcd(long long x,long long y){return !y?x:gcd(y,x%y);} 7 long long f(long long a,long long b,long long c) 8 { 9 long long x=c*1ll/a*1ll,num=0;long long i; 10 for(i=1;i<=x;i++) 11 { 12 if((c*1ll-a*1ll*i)<=0)continue; 13 if((c*1ll-a*1ll*i)%(b*1ll))continue; 14 num++;break; 15 } 16 if(!num)return 0; 17 num+=(x*1ll-i)/b*1ll; 18 if(!((x-i)%b)&&a*x==c&&!(c%a))num--; 19 return num; 20 } 21 int haha() 22 { 23 int t;scanf("%d",&t); 24 while(t--) 25 { 26 long long a,b,c;scanf("%lld%lld%lld",&a,&b,&c); 27 if(a<0)a*=(-1ll),b*=(-1ll),c*=(-1ll); 28 if(a==0) 29 { 30 if(b==0){if(c)puts("0");else puts("ZenMeZheMeDuo");continue;} 31 if(c%b||b*c<0)puts("0");else puts("ZenMeZheMeDuo"); 32 continue; 33 } 34 if(b==0) 35 { 36 if(c%a||a*c<0)puts("0");else puts("ZenMeZheMeDuo"); 37 continue; 38 } 39 long long g=gcd(abs(a),abs(b));if(abs(c)%g){puts("0");continue;}a/=g,b/=g,c/=g; 40 if(a*1ll*b*1ll<0){puts("ZenMeZheMeDuo");continue;} 41 long long ans=max(f(a,b,c),0ll); 42 if(ans<=65535)printf("%lld\\n",ans); 43 else puts("ZenMeZheMeDuo"); 44 } 45 } 46 int sb=haha(); 47 int main(){;}
染色
出门右转：http://www.cnblogs.com/LadyLex/p/7337179.html然而只有我没做过
1 #include<iostream> 2 #include<cstdio> 3 #include<cstring> 4 #include<algorithm> 5 #include<vector> 6 using namespace std; 7 const int maxn=2005; 8 struct node 9 { 10 int from,to,next;long long dis; 11 node(){;} 12 node(int u,int v,long long w,int x):from(u),to(v),dis(w),next(x){;} 13 }edge[maxn<<1]; 14 int head[maxn],tot; 15 void addedge(int u,int v,long long w) 16 { 17 edge[++tot]=node(u,v,w,head[u]);head[u]=tot; 18 } 19 long long f[maxn][maxn],g[maxn]; 20 int n,m,sz[maxn]; 21 void dp(int root,int pa) 22 { 23 sz[root]=1;long long cnt; 24 for(int i=head[root];i;i=edge[i].next) 25 { 26 int v=edge[i].to; 27 if(v!=pa) 28 { 29 dp(v,root); 30 memset(g,0,sizeof(g)); 31 for(int j=0;j<=sz[root];j++) 32 for(int k=0;k<=sz[v];k++)cnt=k*1ll*(m-k)+(sz[v]-k)*1ll*(n-m-(sz[v]-k)),g[j+k]=max(g[j+k],f[root][j]+f[v][k]+cnt*edge[i].dis); 33 sz[root]+=sz[v]; 34 for(int j=0;j<=sz[root];j++)f[root][j]=g[j]; 35 } 36 } 37 } 38 int haha() 39 { 40 scanf("%d%d",&n,&m); 41 for(int i=1;i<n;i++) 42 { 43 int x,y;long long z;scanf("%d%d%lld",&x,&y,&z); 44 addedge(x,y,z);addedge(y,x,z); 45 } 46 dp(1,0);printf("%lld\\n",f[1][m]); 47 } 48 int sb=haha(); 49 int main(){;}
#include<iostream>#include<cstdio>#include<cstring>#include<algorithm>#include<vector>using namespace std;const int maxn=2005;struct node{ int from,to,next;long long dis; node(){;} node(int u,int v,long long w,int x):from(u),to(v),dis(w),next(x){;}}edge[maxn<<1];int head[maxn],tot;void addedge(int u,int v,long long w){ edge[++tot]=node(u,v,w,head[u]);head[u]=tot;}long long f[maxn][maxn],g[maxn];int n,m,sz[maxn];void dp(int root,int pa){ sz[root]=1;long long cnt; for(int i=head[root];i;i=edge[i].next) { int v=edge[i].to; if(v!=pa) { dp(v,root); memset(g,0,sizeof(g)); for(int j=0;j<=sz[root];j++) for(int k=0;k<=sz[v];k++)cnt=k*1ll*(m-k)+(sz[v]-k)*1ll*(n-m-(sz[v]-k)),g[j+k]=max(g[j+k],f[root][j]+f[v][k]+cnt*edge[i].dis); sz[root]+=sz[v]; for(int j=0;j<=sz[root];j++)f[root][j]=g[j]; } }}int haha(){ scanf("%d%d",&n,&m); for(int i=1;i<n;i++) { int x,y;long long z;scanf("%d%d%lld",&x,&y,&z); addedge(x,y,z);addedge(y,x,z); } dp(1,0);printf("%lld\\n",f[1][m]);}int sb=haha();int main(){;}以上是关于一些奇奇怪怪的过题思路的主要内容，如果未能解决你的问题，请参考以下文章