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>
int main(void) {
  int i, k, t, y = 0, z, j, n, m, l = 1000000007;
  double x;
  scanf("%d %d", &m, &n);
  for (i = 1; i <= n; i++) {
    x = pow(m, i);
    if (x > l) {
      z = x;
      j = z % l;
      k = n / i;
      t = n % i;
      y = pow(j, k) * pow(m, t);
      printf("%d", y % l);
      break;
    }
  }
  if (y == 0) {
    z = pow(m, n);
    j = z % l;
    printf("%d", j);
  }
  return 0;
}
