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;
long long gcf(long long a, long long b) {
  if (!a | !b) return 0;
  do {
    if (a < b) swap(a, b);
    a %= b;
  } while (a);
  return b;
}
int main() {
  long long a, b;
  while (cin >> a >> b) {
    cout << gcf(a, b) << endl;
  }
  return 0;
}
