[SDOI2017]数字表格

[SDOI2017]数字表格

https://ac.nowcoder.com/acm/problem/20391

## [SDOI2017]数字表格

```/*
Author : lifehappy
*/
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;

const int N = 1e6 + 10, mod = 1e9 + 7, Mod = mod - 1;

ll prime[N], mu[N], fib[N], phi[N], inv_fib[N], f[N], cnt;

bool st[N];

ll quick_pow(ll a, int n) {
ll ans = 1;
while(n) {
if(n & 1) ans = ans * a % mod;
a = a * a % mod;
n >>= 1;
}
return ans;
}

ll inv(ll a) {
return quick_pow(a, mod - 2);
}

void init() {
fib[1] = mu[1] = f[1] = 1;
for(int i = 2; i < N; i++) {
f[i] = 1;
fib[i] = (fib[i - 1] + fib[i - 2]) % mod;
if(!st[i]) {
prime[++cnt] = i;
mu[i] = -1;
}
for(int j = 1; j <= cnt && 1ll * i * prime[j] < N; j++) {
st[i * prime[j]] = 1;
if(i % prime[j] == 0) {
break;
}
mu[i * prime[j]] = -mu[i];
}
}
for(int i = 1; i < N; i++) {
inv_fib[i] = inv(fib[i]);
}
for(int i = 1; i < N; i++) {
for(int j = i; j < N; j += i) {
if(mu[j / i] == 1) {
f[j] = f[j] * fib[i] % mod;
}
else if(mu[j / i] == -1) {
f[j] = f[j] * inv_fib[i] % mod;
}
}
}
f[0] = 1;
for(int i = 1; i < N; i++) {
f[i] = f[i] * f[i - 1] % mod;
}
}

int main() {
// freopen("in.txt", "r", stdin);
// freopen("out.txt", "w", stdout);
// ios::sync_with_stdio(false), cin.tie(0), cout.tie(0);
init();
int T;
scanf("%d", &T);
while(T--) {
int n, m;
scanf("%d %d", &n, &m);
if(n > m) swap(n, m);
ll ans = 1;
for(int l = 1, r; l <= n; l = r + 1) {
r = min(n / (n / l), m / (m / l));
ans = ans * quick_pow(f[r] * inv(f[l - 1]) % mod, 1ll * (n / l) * (m / l) % Mod) % mod;
}
printf("%lld\n", ans);
}
return 0;
}```

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