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>
long long square(long long x) {
  x = x * x;
  return x;
}
long long bigmod(long long b, long long p, long long m) {
  if (p == 0)
    return 1;
  else if (p % 2 == 0)
    return (square(bigmod(b, p / 2, m))) % m;
  else
    return ((b % m) * bigmod(b, (p - 1), m)) % m;
  return 0;
}
int main() {
  long long b, p, m, mul, y;
  while (scanf("%lld%lld%lld", &b, &p, &m) == 3) {
    y = bigmod(b, p, m);
    printf("%lld\n", y);
  }
  return 0;
}
