For given integers m and n, compute mn (mod 1,000,000,007). Here, A (mod M) is the remainder when A is divided by M.

Constraints

* 1 ≤ m ≤ 100
* 1 ≤ n ≤ 109

Input


m n


Two integers m and n are given in a line.

Output

Print mn (mod 1,000,000,007) in a line.

Examples

Input

2 3


Output

8


Input

5 8


Output

390625
#include <iostream>

using namespace std;

int div(int a, int b, int p)
{
    return ((a%p)*(b%p))%p;
}


int main() {
    const int p = 1000000007;
    int m,n,ans = 0;
    cin >> m >> n;
    int size = (int)log2(n);
    int rem = m;
    for(int i = 0; i < size; i++)
    {
        rem = div(rem,rem,p);
    }
    ans = div(rem,(int)pow(m,n - pow(2,size)),p);
    cout << ans << endl;
    return 0;
}