HDU-5363 Key Set

http://acm.hdu.edu.cn/showproblem.php?pid=5363

Key Set

Time Limit: 2000/1000 MS (Java/Others) Memory Limit: 131072/131072 K (Java/Others)
Total Submission(s): 355 Accepted Submission(s): 233

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

 

 

Source

2015 Multi-University Training Contest 6 

一个（1-n）集合的子集的和是偶数的个数

#include <iostream>
#include <cstdio>
#include <string>
using namespace std;
#define MOD 1000000007
long long ksm(long long x,long long n)
{
    long long pw = 1;
    while (n > 0)
    {
        if (n & 1)        // n & 1 等价于 (n % 2) == 1
            pw =(pw*x+MOD)%MOD;
        x =(x*x+MOD)%MOD;
        n >>= 1;        // n >>= 1 等价于 n /= 2
    }

    return pw;
}
int main()
{
    int t;
    scanf("%d",&t);
    while(t--)
    {
        long long n;
        scanf("%lld",&n);
        n=n-1;
        printf("%lld\n",ksm(2,n)-1);
    }
    return 0;
}