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
p = 1000000007
def modPow(a, n, m):
    ans = 1
    while n > 0:
        if (n & 1): ans = (ans * a) % m
        a = (a * a) % m
        n = n >> 1
    return ans

n, m = map(int, input().split())
print(modPow(n, m, p))
