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 S(x) :
    mod = 1000000007
    return(x % mod)
    
def A(a, b, mod) :
    if b == 1 :
        return a
    elif b%2 == 0 :
        a_2 = S(a**2)
        b_2 = b // 2
        return S(A(a_2, b_2, mod))
    else :
        a_2 = S(a**2)
        b_2 = (b-1) // 2
        return S(A(a_2, b_2, mod)*a)
        
mod = 1000000007
m, n = map(int, input().split())

print(A(m, n, mod))
