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;


int64_t soinbun(int64_t x,int64_t N){
  int64_t n=2;
  int64_t count=0;
  int64_t ans=1;
  while(x>=n*n){
    if(x%n==0){
      x/=n;
      count++;
      if(count==N){
        ans*=n;
        count=0;
      }
    }else{
      n++;
      count=0;
    }
  }
  if(x==n){
    if(count+1==N){
      ans*=n;
    }
  }else{
    if(N==1){
      ans*=x;
    }
  }
  return ans;
}

int main(){
  int64_t N,P;
  cin >> N >> P;
  cout << soinbun(P, N) << endl;
  return 0;
}