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
def pow(a, n, MOD=1):
    """
    繰り返し二乗法 (半分の数の 2 乗) / 自乗
    Compute nth power of a -- O(logn)
    """
    if n == 0:
        return 1
    x = pow(a, n//2, MOD)
    x = (x%MOD * x%MOD) % MOD
    if n%2 == 1:
        x = (x%MOD * a%MOD) % MOD
    return x


MOD = 1_000_000_007
m, n = map(int, input().split())
print(pow(m, n, MOD))
