HDUoj 5363 Key Set (快速幂，数学，规律

                                     Key Set

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 integer T(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

博主对这样例 找了下规律就找到了qaq 

证明 ：
解题思路：因为集合Ｓ中的元素是从１开始的连续的自然数，所以所有元素中奇数个数与偶数个数相同，或比偶数多一个。另外我们要知道偶数＋偶数＝偶数，奇数＋奇数＝偶数，假设现在有ａ个偶数，ｂ个奇数，则
根据二项式展开公式
以及二项式展开式中奇数项系数之和等于偶数项系数之和的定理
可以得到上式
最后的结果还需减去
即空集的情况，因为题目要求非空子集
所以最终结果为

#include<stdio.h>#define N 1000000007#define LL long longLL powMod(LL a, LL b, LL c){LL ans = 1;while(b){if(b&1)ans = (ans*a) % c;a = (a*a) % c;b /= 2;}return ans;}int main(){int  T;scanf("%d",&T);while(T--){LL  a;scanf("%lld",&a);printf("%lld\n",powMod(2,a-1,N)-1);}return 0;}