二次联通门 : BZOJ 4816: [Sdoi2017]数字表格
/* BZOJ 4816: [Sdoi2017]数字表格 莫比乌斯反演 妈呀,我的μ没有啦 */ #include <cstdio> #include <iostream> #define rg register #define Max 1000050 #define mo 1000000007 inline int min (int a, int b) { return a < b ? a : b; } inline void read (int &n) { rg char c = getchar (); for (n = 0; !isdigit (c); c = getchar ()); for (; isdigit (c); n = n * 10 + c - ‘0‘, c = getchar ()); } typedef long long LL; LL f[Max], invf[Max]; LL pow (LL x, LL y) { LL res = 1; for (; y; y >>= 1, (x *= x) %= mo) if (y & 1) (res *= x) %= mo; return res; } inline void pls (LL &a, LL b) { a += b; if (a >= mo) a -= mo; } int main (int argc, char *argv[]) { rg int i, j; LL inv; int N, M, T; f[1] = 1; for (i = 2; i < Max; ++ i) pls (f[i], f[i - 1] + f[i - 2]); for (i = 1; i < Max; ++ i) { inv = pow (f[i], mo - 2); for (j = i << 1; j < Max; j += i) (f[j] *= inv) %= mo; } for (f[0] = i = 1; i < Max; ++ i) (f[i] *= f[i - 1]) %= mo; for (i = 0; i < Max; ++ i) invf[i] = pow (f[i], mo - 2); read (T); LL Answer; for (; T; -- T) { read (N), read (M); Answer = 1; if (N > M) std :: swap (N, M); for (i = 1; i <= N; i = j + 1) { j = min (N / (N / i), M / (M / i)); (Answer *= pow (pow (f[j] * invf[i - 1] % mo, (LL) N / i), (LL) M / i)) %= mo; } printf ("%lld\n", Answer); } return 0; }