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
main = do
    [m,n] <- fmap (map read.words) getLine
    print $ powMod 1000000007 m n

powMod :: Int -> Int -> Int -> Int
powMod _ _ 0 = 1
powMod p m n
  | even n =let x' = powMod p m (n `div` 2) in x'^2 `mod` p
  | odd n = let x' = powMod p m ((n-1) `div` 2) in m*x'^2 `mod` p

