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: Runtime Error)

import qualified Data.Map as Map

scan :: Int -> Int -> Int
scan _ 1 = 1
scan 1 p = p
scan n p = Map.foldrWithKey f 1 (factors (root n p) p) where
    f k a b = b * (k^(div a n))

factors :: Int -> Int -> Map.Map Int Int
factors l n = iter Map.empty (primesL l) where
    iter m [] = m
    iter m (p:ps) = case logP p n of
        Just e -> iter (Map.insert p e m) ps
        Nothing -> iter m ps

logP :: Int -> Int -> Maybe Int
logP p n = if mod n p == 0 then iter 0 n else Nothing where
        iter e x = case divMod x p of
            (1, 0) -> Just (e+1)
            (q, 0) -> iter (e+1) q
            (_, _) -> Just e                

root :: Int -> Int -> Int
root n p = iter 0 (10^(1 + div 12 n)) where
    iter s e
        | e - s == 1 = e
        | m ^ n < p = iter m e
        | otherwise = iter s m 
        where m = div (s+e) 2

primesL :: Int -> [Int]
primesL n = 2:(sieve [3,5..n]) where
    sieve (x:xs)
        | root 2 n >= x = x : sieve (filter (\y -> mod y x /=0) xs)
        | otherwise    = x:xs
{- 
primes :: [Int]
primes = 2:(sieve [3,5..]) where
    sieve (x:xs) = x : sieve (filter (\y -> mod y x /=0) xs)
 -}                
main :: IO() 
main = do
    line1 <- getLine
    let [stN, stP] = words line1
        n = read stN :: Int
        p = read stP :: Int
    let ans = scan n p
    print ans