hdu 3923 Invoker polya 定理

/*
 * hdu3923.c
 *
 *  Created on: 2011-9-20
 *      Author: bjfuwangzhu
 */

#include<stdio.h>
#include<math.h>
#define LL long long
#define nnum 1000000007
LL x, y;
LL modular_exp(int a, int b) {
    LL res, temp;
    res = 1 % nnum,temp = a % nnum;
    while (b) {
        if (b & 1) {
            res = res * temp % nnum;
        }
        temp = temp * temp % nnum;
        b >>= 1;
    }
    return res;
}
int getPhi(int n) {
    int phi, i, te;
    te = (int) (sqrt(n * 1.0));
    for (i = 2, phi = n; i <= te; i++) {
        if (n % i == 0) {
            phi = phi / i * (i - 1);
            while (n % i == 0) {
                n /= i;
            }
        }
    }
    if (n > 1) {
        phi = phi / n * (n - 1);
    }
    return phi;
}
void extend_gcd(int a, int b) {
    if (b == 0) {
        x = 1LL, y = 0;
        return;
    }
    extend_gcd(b, a % b);
    LL tx = x;
    x = y, y = tx - a / b * y;
}
LL polya(int n, int m) {
    int i;
    LL sum;
    for (i = 1, sum = 0; i <= m; i++) {
        if (m % i == 0) {
            sum += modular_exp(n, i) * getPhi(m / i) % nnum;
            sum %= nnum;
        }
    }
    if (m & 1) {
        sum += modular_exp(n, (m + 1) / 2) * m % nnum;
        sum %= nnum;
    } else {
        sum += modular_exp(n, m / 2) * (m / 2) % nnum;
        sum %= nnum;
        sum += modular_exp(n, m / 2 + 1) * (m / 2) % nnum;
        sum %= nnum;
    }
    extend_gcd(m << 1, nnum);
    x = (x % nnum + nnum) % nnum;
    sum = sum * x % nnum;
    return sum;
}
int main() {
#ifndef ONLINE_JUDGE
    freopen("data.in", "r", stdin);
#endif
    int i, t, n, m;
    LL sum;
    while (~scanf("%d", &t)) {
        for (i = 1; i <= t; i++) {
            scanf("%d %d", &n, &m);
            sum = polya(n, m);
            printf("Case #%d: %I64d\n", i, sum);
        }
    }
    return 0;
}