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 check(a,b):
    temp = 1
    for i in range(b):
        temp = temp*a
        if temp >= 1000000007:
            break
    return (i+1)
        
def cul(a,b,i):
    temp = b % i
    answer = b // i
    test = (a**i)%1000000007
    t = 1
    for i in range(answer):
        t = (test*t)%1000000007
    return (t*(a**temp)%1000000007)

a,b = map(int, input().strip().split(' '))
print(cul(a,b,check(a,b)))

