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: Wrong Answer)

main = do
  (n:p:xs) <- (map read) . words <$> getLine
  putStrLn . show $ solve n p


solve :: Integer -> Integer -> Integer
solve num p = calcFactors num p primeList
  where
    calcFactors :: Integer -> Integer -> [Integer] -> Integer
    calcFactors n 1 primes = 1
    calcFactors n prod (pr:primes) =
      let nd = nDiv prod pr
      in if pr * n > prod || (pr^2 > p) then 1 else
        (pr ^ (nd `div` n)) * (calcFactors n (prod `div` (pr^nd)) primes)

nDiv x pr = if x `mod` pr == 0 then 1 + (nDiv (x `div` pr) pr) else 0

--primeList :: Integral a => a
primeList = 2 : prime'
prime' = 3 : 5 : 7 : (siege 3 prime')
siege m (a:b:xs) = [n|n<-[a^2,a^2+2..b^2-2],gcd n m<2] ++ (siege (m*b) (b:xs))