2017 ACM-ICPC 亚洲区（西安赛区）网络赛： B. Coin

Bob has a not even coin, every time he tosses the coin, the probability that the coin’s front face up is qp ( qp ≤12 )
The question is, when Bob tosses the coin kk times, what’s the probability that the frequency of the coin facing up is even number.

If the answer is XY ​​ , because the answer could be extremely large, you only need to print (X∗Y−1)mod(109+7).

Input Format

First line an integer T, indicates the number of test cases ( T≤100 ).

Then Each line has 3 integer p,q,k( 1≤p,q,k≤107 ) indicates the i-th test case.

Output Format

For each test case, print an integer in a single line indicates the answer.

样例输入

2
2 1 1
3 1 2
样例输出

500000004
555555560

思路:一个高中的组合数学题。。。。。

ans=∑i=0i∗2≤k(qp)2i(1−qp)(k−2i)C2ik

ans=1pk∑i=0i∗2≤kq2i(p−q)(k−2i)C2ik

ans=1pk((p−q)+q)k+((p−q)−q)k2

#include
using namespace std;
const int MOD=1e9+7;
long long POW(long long x,long long n)
{
    long long res=1;
    while(n)
    {
        if(n&1)res=(res*x)%MOD;
        x=(x*x)%MOD;
        n/=2;
    }
    return res;
}
int main()
{
    int T;cin>>T;
    while(T--)
    {
        long long p,q,k;
        scanf("%lld%lld%lld",&p,&q,&k);
        long long x=POW(p-2*q,k);
        long long y=POW(p,k);
        cout<<(  ((1+x*POW(y,MOD-2))%MOD) * POW(2,MOD-2) )%MOD<return 0;
}