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)

//submitted by Himj
#include<bits/stdc++.h>
#define ll long long
#define mod 1000000007
#define pb push_back
#define fi first
#define se second
#define fr(i,s,e) for(i=s;i<e;i++)
#define ms(arr,val) memset(arr,val,sizeof(arr))
using namespace std;

const int mxn=2e5+1;

int main(){
    ios_base::sync_with_stdio(false);
    cin.tie(0);
    cout.tie(0);
#ifndef ONLINE_JUDGE
freopen("input.txt", "r", stdin);
freopen("output.txt", "w", stdout);
#endif
  int t=1;
  //cin>>t;
    while(t--){
      ll n,p,i,j,ans=1;
      cin>>n>>p;
      j=2;
      while(j*j<=p)
      {
        ll cnt=0;
        while(p%j==0)
        {
          p/=j;
          cnt++;
        }
        ans*=pow(j,cnt/n);
        j++;
      }
      if(n==1)
        ans*=p;
      cout<<ans;

      
       
    }
  return 0;
  }