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 <bits/stdc++.h>
using namespace std;
int main() {
  unsigned long long int m, n;
  const unsigned long long int p = 1000000007;
  cin >> m >> n;
  int i = 2;
  while (n > 1) {
    if (n % i != 0) {
      i++;
      continue;
    }
    n /= i;
    for (int j = 0; j < i - 1; j++) {
      m *= m;
      m %= p;
    }
  }
  cout << m << endl;
  return 0;
}
