P4240 毒瘤之神的考验

Posted 2021-12-06 willems

题目： https://www.luogu.org/problemnew/show/P4240

 

解：神仙 题  化出了式子了 还要会构造函数，构造了函数 还要会实现。  牛逼儿~~~   （ 出处：https://www.cnblogs.com/y2823774827y/p/10235949.html ）

 

 

 

 

#include<bits/stdc++.h>
#define LL long long
#define ULL unsigned long long
#define rep(i,j,k) for(int i=j;i<=k;i++)
#define dep(i,j,k) for(int i=k;i>=j;i--)
#define INF 0x3f3f3f3f
#define mem(i,j) memset(i,j,sizeof(i))
#define make(i,j) make_pair(i,j)
#define pb push_back
using namespace std;
const int block=35;
const int N=1e5+9;
const LL p=998244353;
bool vis[N];
int mu[N],phi[N],pre[N];
int *G[N],*S[block+1][block+1],F[N];
int inv[N],tot;
void init() {
    mu[1]=phi[1]=inv[1]=1;
    rep(i,2,100000) {
        if(!vis[i]) {
            pre[++tot]=i; mu[i]=-1; phi[i]=i-1;
        }
        rep(j,1,tot) {
            if(i*pre[j]>100000) break;
            vis[i*pre[j]]=true;
            if(i%pre[j]==0) {
                phi[i*pre[j]]=phi[i]*pre[j]; break;
            }
            else {
                phi[i*pre[j]]=phi[i]*phi[pre[j]];
                mu[i*pre[j]]=-mu[i];
            }
        }
    }
    rep(i,2,100000) inv[i]=p-1LL*p/i*inv[p%i]%p;
    rep(i,1,100000) {
        for(int j=1;j*i<=100000;j++) {
            F[i*j]=1LL*(1LL*F[i*j]+1LL*i*inv[phi[i]]%p*mu[j]%p)%p;
        }
    }
    rep(i,1,100000) {
        G[i]=new int [N/i+1];
        G[i][0]=0;
        rep(j,1,100000/i) {
            G[i][j]=1LL*(1LL*G[i][j-1]+1LL*phi[i*j])%p;
        }
    }
    rep(j,1,block) {
        rep(k,1,block) {
            int len(100000/(max(k,j)));
            S[j][k]=new int [len+1];
            S[j][k][0]=0;
            rep(i,1,len) {
                S[j][k][i]=1LL*(1LL*S[j][k][i-1]+1LL*F[i]*G[i][j]%p*G[i][k]%p)%p;
            }
        }
    }
}
LL cal(int n,int m) {
    if(n>m) swap(n,m);
    LL ans=0;
    for(int i=1;i<=m/block;i++) ans=(ans+1LL*F[i]*G[i][n/i]%p*G[i][m/i]%p)%p;
    for(int l=m/block+1,r;l<=n;l=r+1) {
        r=min(n/(n/l),m/(m/l));
        ans=(ans+1LL*(S[n/l][m/l][r]-S[n/l][m/l][l-1]+p)%p)%p;
    }
    return ans;
}
int main() {
    init();
    int t;
    scanf("%d",&t);
    while(t--) {
        int n,m;
        scanf("%d %d",&n,&m);
        printf("%lld\\n",cal(n,m));
    }
    return 0;
}

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