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: Wrong Answer)

#include <iostream>
#include <algorithm>
#include <string>
#include <vector>
#include <cmath>
#include <map>
#include <queue>
#include <iomanip>
#define MOD 1000000007
typedef long long ll;
using namespace std;

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

  map<ll,ll> mp;
  ll ans=1,last=0;
  for(int i=2;i*i<=p;i++){
    if(p%i==0){
      ll tmp=0;
      while(p%i==0){
        tmp++;
        p/=i;
      }
      mp[i]=tmp;
    }
    if(mp[i]>=n){
      ans*=i;
      last=i;
    }
  }

  if(p!=1) mp[p]++;
  if(mp[p]>=n&&last!=p){
    ans*=p;
  }

  cout<<ans<<endl;


  return 0;
}