2015 多校联赛 ——HDU5363（快速幂）

 

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 of S 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

4 1 2 3 4

 

 

Sample Output

0 1 3 7

 

 

给你一个1-n的集合，问你有多少个子集的元素和为偶数

假设偶数有a个，奇数有b个,总数为n：

偶：C（0, a）+ C（1 , a）....... + C（a, a） =   2 ^ a

奇：C（0, b）+ C（2 , b）....... + C（b, b） = 2 ^ (b - 1)

all =  偶 * 奇 - 1（奇偶中都不选的情况）；

--->   all  =  2 ^ (a + b - 1)- 1   =   2 ^ (n - 1) -1

#include <iostream>
#include <cstdio>
#include <vector>
#pragma comment(linker, "/STACK:102400000,102400000")
using namespace std;
typedef long long ll;
char ma[1100][1100];
int ln, lm;
const int mod = 1000000007;

ll pow_mod(int a,int n)
{
    if(n == 0)
        return 1;
    ll x = pow_mod(a,n/2);
    ll ans = (ll)x*x%mod;
    if(n %2 == 1)
        ans = ans *a % mod;
    return ans;
}

int main()
{
    int T;
    scanf("%d",&T);
    while(T--)
    {
        int n;
        scanf("%d",&n);

        ll sum1 = (pow_mod(2,n-1)-1)%mod;
        printf("%I64d\n",sum1);
    }

    return 0;
}