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)

primes :: [Int]
primes = sieve (2 : [3, 5..])
  where
    sieve (p:xs) = p : sieve [ x | x <- xs, x `mod` p > 0]

eff_prime::Int->Int->[Int]
eff_prime n p = takeWhile (large n p) primes

eater::Int->Int->[Int]->Int
eater n p []    = 1
eater n p (pr:prs)= let (p',k) = (multi_div p pr) in (pr^(div k n))*(eater n p' prs)

large::Int->Int->Int->Bool
large n p pr =  n <= (loga pr p)


loga::Int->Int->Int
loga k l = if k > l then 0 else 1 + (loga k (div l k))

multi_div::Int->Int->(Int,Int)
multi_div n divider = if mod n divider /= 0
                        then (n,0)
                        else let (q,i) = multi_div (div n divider) divider in (q,i+1)

solver::Int->Int->Int
solver n p  = eater n p (eff_prime n p)

main::IO()
main=do
  d<-getLine
  let n:p:[]=map read (words d)
  print (solver n p)