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
import Control.Applicative

func a 0 = 1
func a b = (a * (func a (b-1))`mod`1000000007)

main = do{
    [a,b] <- map (read::String->Integer) . words <$> getLine;
    putStrLn $ show $ func a b;
}