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
from functools import lru_cache
@lru_cache(maxsize=None)

def power(a, b):
    res = 1
    # print(a, b)
    if b > 0:
        res = power(a, b // 2)
        if b % 2 == 0:
            res = (res * res) % 1000000007
        else:
            res = (((res * res) % 1000000007) * a) % 1000000007
    
    return res
    
m, n = map(int, input().split())

print(power(m, n))
