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 <map>
#include <algorithm>
using namespace std; typedef long long ll; const int INF=1e9+7;
typedef pair<int,int> P;

int main() {
  ll n,p; cin>>n>>p;
  map<ll,ll> mp;
  for(ll i=2;i*i<=p;i++) {
    while(p%i==0) p/=i, mp[i]++;
  }
  mp[p]++;

  ll an=1;
  for(P x:mp) {
    for(int i=0;i<x.second/n;i++) {
      an*=x.first;
    }
  }
  cout<<an<<endl;
}