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 C++14 (GCC 5.4.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
using namespace std;

bool memo[1000010] = {};

queue<int> que;

int main(){
  long long n, p;
  cin >> n >> p;

  for(int i = 2;i < 1000010;i++){
    if(!memo[i]){
      que.push(i);
      for(int j = i*2;j < 1000010;j+=i){
        memo[j] = true;
      }
    }
  }

  long long work = p;

  long long ans = 1;
  int ww = que.front();
  que.pop();

  int atmp = 0;
  while(work > 1 && !que.empty()){
    if(work % ww == 0){
      atmp++;
      if(atmp == n){
        ans *= ww;
        atmp = 0;
      }
      work /= ww;
    }else{
      atmp = 0;
      ww = que.front();
      que.pop();
    }
  }

  if(work == 1){
    cout << ans << endl;
  }else{
    if(n == 1){
      cout << p << endl;
    }else{
      cout << ans << endl;
    }
  }

  return 0;
}