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: Accepted)

from collections import Counter
import sys
sys.setrecursionlimit(1000000)

def solve():
  n,p = (int(i) for i in input().split())
  ans = 1
  if n == 1:
    print(p)
    exit()
  p_dummy = p
  for i in range(2,int(p_dummy**0.5)+4):
    ct = 0
    while p_dummy%i == 0:
      ct += 1
      p_dummy //= i
      if ct >= n:
        ans *= i
        ct -= n
  

  print(ans)
  
solve()