Problem E
Teams

Input: Standard Input

Output: Standard Output

In a galaxy far far away there is an ancient game played among the planets. The specialty of the game is that there is no limitation on the number of players in each team, as long as there is a captain in the team. (The game is totally strategic, so sometimes less player increases the chance to win). So the coaches who have a total of N

players to play, selects K (1 ≤ K ≤ N) players and make one of them as the captain for each phase of the game. Your task is simple, just find in how many ways a coach can select a team from his N players. Remember that, teams with same players but having different captain are considered as different team.

Input

The first line of input contains the number of test cases T ≤ 500. Then each of the next T lines contains the value of N (1 ≤ N ≤ 10^9), the number of players the coach has.

Output

For each line of input output the case number, then the number of ways teams can be selected. You should output the result modulo 1000000007.

For exact formatting, see the sample input and output.

Sample Input                                                                               Output for Sample Input

3 1 2 3

Case #1: 1 Case #2: 4 Case #3: 12

Problem Setter: Towhidul Islam Talukdar

Special Thanks: Md. Arifuzzaman Arif

    解題報告：大水題。先從n個人中選出冠軍，一共n種選法。其他人在或者不在，都是兩種情況，一共2^(n-1)種情況。二分快速冪一下。程式碼如下：

#include <cstdio>
#include <cstring>
#include <algorithm>
using namespace std;

const int mod = 1000000007;
typedef long long LL;

LL powMod(LL a, LL b)
{
    LL res=1;
    while(b)
    {
        if(b&1)
            res = res*a%mod;
        a=a*a%mod;
        b>>=1;
    }
    return res;
}

int cas=1;
void work()
{
    int n;
    scanf("%d",&n);
    printf("Case #%d: %lld\n", cas++, powMod(2, n-1)*n%mod);
}

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