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 $ calcMod m n 

calcMod m n = (recPow m n) `mod` 1000000007

recPow :: Integer -> Integer -> Integer
recPow m n
  | n == 0 = 1
  | even n = recPow (m^2) (n `div` 2)
  | otherwise = m * recPow (m^2) (n `div` 2)