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
a,b = map(int,input().split())
def pow_k(x, n):
    """
    O(log n)
    """
    if n == 0:
        return 1

    K = 1
    while n > 1:
        if n % 2 != 0:
            K *= x
        x *= x
        n //= 2

    return K * x
print(pow(a,b,1000000007))
