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
include <stdio.h>
include <stdio.h>
	int main(){
 	int S,h,m,s;
	cin>>S>>h>>m>>s;
	h=S/3600;
	m={S-(h*3600)}/60; 
	s=S-(h*3600+m*60);	
	cout<<h<<m<<s;endl;}