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(m,n,res)
	if n%2==1
			res=res*m
			m=m*m
			n=n/2
	else
			m=m*m
			n=n/2
	end
	return m,n,res
end
m,n=gets.chomp.split(" ").map{|i| i.to_i}
res=1

	while n>1
		m,n,res=pow(m,n,res)
	end

puts m*res%1000000007