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
def mpow(x,n):
    if n == 0:
        return 1
    if n % 4 == 0:
        return mpow(x**4,int(n/4))
    elif n%4 == 1:
        return mpow(x,int(n-1))*x
    elif n%4 == 2:
        return mpow(x,int(n-2))*x*x
    elif n%4 == 3:
        return mpow(x,int(n-3))*x*x*x
n,m = map(int,input().split())
x = 1000000007
print(mpow(n,m)%x)