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 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;
}
