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: Accepted)

import Control.Arrow
import Control.Monad
import Data.List
import qualified Data.ByteString.Char8 as B

main :: IO ()
main = readLine >>= print . solve 

solve :: [Int] -> Int 
solve [n, p]
    | n == 1 || p == 1 = p
    | otherwise = pf 1 [2..(truncate . sqrt $ fromIntegral p)] n p
    
pf :: Int -> [Int] -> Int -> Int -> Int
pf acc (x : xs) n p
    | p == 1 = acc
    | y == 0 = pf acc xs n q
    | otherwise = pf (acc * (x ^ y)) xs n q
    where
        y = z `div` n
        (q, z) = count p x
pf acc _ _ _ = acc 

count :: Int -> Int -> (Int, Int)
count v x = loop 0 m
    where
        m = truncate . succ . logBase (fromIntegral x) $ fromIntegral v
        loop b t
            | t - b < 2 = (v `div` bv, b)
            | v `mod` hv == 0 = loop h t
            | otherwise = loop b h
            where
                h = (b + t) `div` 2
                bv = x ^ b
                hv = x ^ h

readLine :: IO [Int]
readLine = unfoldr (\s -> second (maybe B.empty snd . B.uncons) <$> B.readInt s) <$> B.getLine

readContents :: Int -> IO [[Int]]
readContents = flip replicateM readLine