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 Python (3.4.3) (judge verdict: Time Limit Exceeded)

import functools
import operator

N,P = map(int,input().split())

i = 2
res = []
if N == 1:
  print(P)
elif P == 1:
  print(1)
else:
  while i <= P**1/N:
    while P % i**N == 0:
      P /= i**N
      res.append(i)
    else:
      if i == 2:
        i += 1
      else:
        i += 2
  res.append(1)
  result = functools.reduce(operator.mul, res)
  print(result)
  exit()