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# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;

class P{

    static void Main(){
       List<long>Sosu=new List<long>{2};
       var s=Console.ReadLine().Split().Select(long.Parse).ToArray();
       if(s[0]==1){
           Console.WriteLine(s[1]);
       }
       long lim=1+(long)Math.Pow((double)s[1],0.5/s[0]);
       for(long i=3;i<=lim;i++){
           if(Sosu.All(x=>i%x!=0))Sosu.Add(i);
       }
       int Lsosu=Sosu.Count();
       long[] cd=Enumerable.Repeat(0L,Lsosu).ToArray();
       for(int i=0;i<Lsosu;i++){
           while(s[1]%Sosu[i]==0){
               s[1]/=Sosu[i];
               cd[i]++;
           }
       }
       long ans=1;
       for(int i=0;i<Lsosu;i++){
           ans*=(long)Math.Pow((double)Sosu[i],(double)(cd[i]/s[0]));
       }
       Console.WriteLine(ans);
    }
}