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
tuplify :: [Int] -> (Int, Int)
tuplify [x, y] = (x, y)

solve :: (Int, Int) -> Int
solve (x, y) = x^y `mod` 1000000007


main = do
    a <- getLine
    putStrLn $ show $ solve $ tuplify ( map read (words a) :: [Int] )