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 Data.Int

main = getLine >>= print . solve 1 . map (read :: String -> Int64) . words

solve :: Int64 -> [Int64] -> Int64
solve ans [_, 0] = ans
solve ans [n, m] = if m `mod` 2 == 1
                   then solve (ans * n `mod` 1000000007) [n * n, m `div` 2]
                   else solve ans [n * n, m `div` 2]