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

solve :: Integer -> Integer -> Integer
solve x y = powerfulPower (x, y) `mod` 1000000007

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

powerfulPower :: (Integer, Integer) -> Integer
powerfulPower (x, y) 
    | (y == 0) = 1
    | even y = powerfulPower (x*x, y`div`2)
    | odd y = x * powerfulPower (x*x, y`div`2)