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 pow(x,n)
	if n==0
		return 1
	elsif n.even?
		res=pow(x*x,n/2)
	else
		res=pow(x*x,n/2)*x
	end
end
m,n=gets.chomp.split(" ").map{|i| i.to_i}

puts pow(m,n)%1000000007