Problem:
Score : 300 points

Problem Statement

There are N integers a_1, a_2, ..., a_N not less than 1.
The values of a_1, a_2, ..., a_N are not known, but it is known that a_1 \times a_2 \times ... \times a_N = P.

Find the maximum possible greatest common divisor of a_1, a_2, ..., a_N.

Constraints

1 \leq N \leq 10^{12}

1 \leq P \leq 10^{12}

Input

Input is given from Standard Input in the following format:

N P

Output

Print the answer.

Sample Input 1

3 24

Sample Output 1

2

The greatest common divisor would be 2 when, for example, a_1=2, a_2=6 and a_3=2.

Sample Input 2

5 1

Sample Output 2

1

As a_i are positive integers, the only possible case is a_1 = a_2 = a_3 = a_4 = a_5 = 1.

Sample Input 3

1 111

Sample Output 3

111

Sample Input 4

4 972439611840

Sample Output 4

206

Solution in Haskell (GHC 7.10.3) (judge verdict: Time Limit Exceeded)

import qualified Data.Map.Strict as Map

primeFactorize :: Integer -> [Integer]
primeFactorize 1 = []
primeFactorize x =
    let v = head $ nativeFactors x in
        v : primeFactorize (x `div` v)
    where
        nativeFactors n = [a | a <- [2..n], n `mod` a == 0]

toCountMap :: (Ord k, Integral a) => [k] -> Map.Map k a
toCountMap xs = Map.fromListWith (+) $ zip xs (repeat 1)

main :: IO ()
main = do
    (n:p:_) <- fmap (map read . words) getLine :: IO[Integer]
    print $ solve n p

solve :: Integer -> Integer -> Integer
solve n p =
    let ps = Map.toList $ toCountMap $ primeFactorize p
    in foldr (\ (x, e) total -> total * (x ^ (e `div` n))) 1 ps