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++ (GCC 9.2.1) (judge verdict: Runtime Error)

#include <bits/stdc++.h>
#define rep(i,n) for (int i = 0; i < (n); i++)
#define sz(x) int(x.size())
using namespace std;
typedef long long ll;
const int inf = 1001001001;

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

  int m = sqrt(p);
  vector<ll> d(m+1);
  rep(i,m+2) d[i]=0;

  ll j = 2;
  while(1){
    if(p%j == 0){
      p /= j;
      d[j]++;
      continue;
    }
    j++;
    if(j > m+1) break;
  }

  ll ans = 1;
  for(int i = 2; i <= m+1; i++) {
    ll k = d[i]/n;
    if(!k) continue;
    ans *= i*k;
    //cout << i << " " << d[i] << endl;
  }
  if(1/n == 1) ans *= p;
  
  cout << ans << endl;
  
}