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
a=1000000007

def isuu(m,n):
    result=1
    i=0
    while i<n:
        result=(result*m)%a
        if result==1:
            return [0,i]
        i+=1
    return [1,result]


m,n=[int(i) for i in input().split(" ")]

i=isuu(m,n)
if i[0]==1:
    print(i[1])
else:
    print((m**(n%i[1]))%a)