hdoj5363Key Set

Problem Description

soda has a set S with n integers {1,2,…,n}. A set is called key set if the sum of integers in the set is an even number. He wants to know how many nonempty subsets ofS are key set.

 

Input

There are multiple test cases. The first line of input contains an integerT(1≤T≤105), indicating the number of test cases. For each test case:

The first line contains an integer n(1≤n≤109), the number of integers in the set.

 

Output

For each test case, output the number of key sets modulo 1000000007.

 

Sample Input

41234

 

Sample Output

0137

 

Author

zimpha@zju

 题意：给你一个具有n个元素的集合s{1，2，3，4，，，，n}，问该集合的非空子集中和为偶数的非空子集的个数。经过推导，sum=2^(n-1)-1;

此题需要用到快速幂（用于求2^(n-1));

代码如下：

#include<cstdio>#include<cstring>#include<algorithm>#define LL long longusing namespace std;  const int mod = 1000000007;LL quickpow(LL n,LL m){int ans=1;while(m){if(m&1){ans=n*ans%mod;}n=n*n%mod;m>>=1;}return ans;}int main(){int n;scanf("%d",&n);while(n--){LL q;scanf("%lld",&q);LL sum=quickpow(2,q-1)-1;printf("%lld\n",sum);}}