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 Debug.Trace

main = do
    [n,p] <- map read . words <$> getLine :: IO [Int]
    let candMax =  ceiling $ (fromIntegral p) ** (1 / (fromIntegral n))
    print $ solve p n candMax

solve :: Int -> Int -> Int -> Int
solve p n i 
    | i == 1 = 1 
    | amari == 0 = i
    | otherwise = solve p n (i-1)
    where 
        temp = i^n
        amari = p `mod` temp