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
    str <- getLine
    let [a, b] = map read $ words $ str :: [Int]
    solve a b
solve :: Int -> Int -> IO ()
solve a b = do
    if (b /= 1)
        then if (odd b)
            then do solve ((a * a * 2) `mod` 1000000007) (b `div` 2)
            else solve ((a * a) `mod` 1000000007) (b `div` 2)
        else do  putStrLn $ show a