017 ACM-ICPC 亚洲区（西安赛区）网络赛 Coin 概率+矩阵快速幂

#include <bits/stdc++.h>
using namespace std;
typedef long long LL;
const LL mod = 1e9+7;
struct Matrix{
    LL a[2][2];
    void set1(){
        memset(a, 0, sizeof(a));
    }
    void set2(){
        set1();
        for(int i=0; i<2; i++) a[i][i]=1;
    }
};
Matrix operator*(const Matrix &a, const Matrix &b){
    Matrix res;
    res.set1();
    for(int i=0; i<2; i++){
        for(int j=0; j<2; j++){
            for(int k=0; k<2; k++){
                res.a[i][j] = (res.a[i][j] + a.a[i][k]*b.a[k][j]%mod)%mod;
            }
        }
    }
    return res;
}
Matrix qsm(Matrix a, LL n){
    Matrix res;
    res.set2();
    while(n){
        if(n&1) res = res*a;
        a = a*a;
        n /= 2;
    }
    return res;
}
LL qsmrev(LL a, LL n){
    LL ret = 1;
    while(n){
        if(n&1) ret=ret*a%mod;
        a=a*a%mod;
        n/=2;
    }
    return ret;
}

int main()
{
    int T;
    scanf("%d", &T);
    while(T--){
        LL p, q, k;
        scanf("%lld %lld %lld", &p,&q,&k);
        LL up = q*qsmrev(p, mod-2)%mod;
        LL down = (p-q)*qsmrev(p, mod-2)%mod;
        Matrix a, b;
        a.set1();
        a.a[0][0]=down;
        a.a[1][0]=up;
        if(k==1){
            printf("%lld\n", a.a[0][0]);
        }
        else{
            b.a[0][0]=down, b.a[0][1]=up;
            b.a[1][0]=up, b.a[1][1]=down;
            a = qsm(b, k-1)*a;
            printf("%lld\n", a.a[0][0]%mod);
        }
    }
    return 0;
}