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: Runtime Error)

#include <iostream>
#include <vector>
using namespace std;

vector <long long> divide(100001,1);

long long power(long long a,long long p){long long s;
  if(p==1) return a;
  if(p==2)
    return a*a;
  if(p%2==0){
    s =power(a,p/2);
    return s*s;
    
  }
  else {s=power(a,p/2);return s*s*a;}
  
}

int main(){//cout<<123<<endl;
  long long N,P;
  cin>>N>>P;
  long long ans=0;
  long long judge=1;
  long long flag=0;
  long long save=1;
  bool de=true;
  for(ans=1;flag<=P;ans++){
    for(int k=1;k<=judge;k++){
      if(P%divide.at(k)!=0) {de=false;break;}
    }
    if(!de) {de=true;continue;}
    long long pre=power(ans,N);
    if(P%pre==0) save=ans;
    else{
      divide.at(judge)=ans;
      judge++;
    }
    flag=pre;
   // cout<<pre<<endl;
  }
  cout<<save<<endl;
return 0;
}