2017多校训练Contest2: 1006 Funny Function hdu6050

Problem Description

Function Fx,ysatisfies:

For given integers N and M,calculate Fm,1 modulo 1e9+7.

 

Input

There is one integer T in the first line.
The next T lines,each line includes two integers N and M .
1<=T<=10000,1<=N,M<2^63.

 

Output

For each given N and M,print the answer in a single line.

 

Sample Input

2
2 2
3 3

 

Sample Output

2
33

推导如下

F1i=2^i-(-1)^i/3
Fij=F(i+n)-F(i)
Fm1=sum(C(m-1,i)*2^i*(-1)^(m-1-i))
=(2*(2^n-1)^(m-1)+n%2)/3

#include<map>
#include<cmath>
#include<queue>
#include<vector>
#include<cstdio>
#include<string>
#include<cstring>
#include<cassert>
#include<iostream>
#include<algorithm>
using namespace std;
long long mod=1000000007;
inline long long power(long long x,long long y)
{
	long long t=1;
	while(y!=0)
	{
		if(y%2==1)
			t=t*x%mod;
		x=x*x%mod;
		y/=2;
	}
	return t;
}
int main()
{
	int T;
	scanf("%d",&T);
	while(T>0)
	{
		T--;
		long long n,m;
		scanf("%lld%lld",&n,&m);
		long long ans=power(2,n)-1LL;
		ans=power(ans,m-1);
		ans=ans*2LL%mod;
		ans+=n%2;
		long long xt=power(3,mod-2);
		ans=ans*xt%mod;
		printf("%lld\n",ans);
	}
	return 0;
}

Problem Description

Function Fx,ysatisfies:

For given integers N and M,calculate Fm,1 modulo 1e9+7.

 

Input

There is one integer T in the first line.
The next T lines,each line includes two integers N and M .
1<=T<=10000,1<=N,M<2^63.

 

Output

For each given N and M,print the answer in a single line.

 

Sample Input

2
2 2
3 3

 

Sample Output

2
33