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
import math
m, n = map(int, raw_input().split())
if m > 1:
    nlm = n * math.log(m,10)
    la = math.log(1000000007)
    nlm -= int(nlm/la)*la
    print int(10**(nlm+1.e-10))
else:
    print 0