小D的Lemon

小D的Lemon

这里还是给出的朴素版本地写法...

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

using namespace std;

const int N = 3e5 + 10, mod = 1e9 + 7, Mod = mod - 1;

int prime[N], g[N], invg[N], mu[N], cnt;

bool st[N];

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

int inv(int x) {
    return quick_pow(x, mod - 2);
}

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

int calc(int n, int m) {
    int ans = 0;
    for(int l = 1, r; l <= n; l = r + 1) {
        r = min(n / (n / l), m / (m / l));
        ans = (ans + 1ll * (mu[r] - mu[l - 1]) * (n / l) % Mod * (m / l) % Mod + Mod) % Mod;
    }
    return ans;
}

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);
        int ans = 1;
        for(int l = 1, r; l <= n; l = r + 1) {
            r = min(n / (n / l), m / (m / l));
            ans = 1ll * ans * quick_pow(1ll * g[r] * invg[l - 1] % mod, calc(n / l, m / l)) % mod;
        }
        printf("%d\n", ans);
    }
    return 0;
}