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
d = 1000000007

def pow_rem(x, n):
    if n == 0:
        return x ** n % d
    if n % 2 == 0:
        return pow_rem(x, n // 2) ** 2 % d
    else:
        return ((pow_rem(x , n // 2) ** 2) * x) % d

def solve():
    m, n = map(int, input().split())
    print(pow_rem(m, n)

solve()