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: Accepted)

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

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		if(P == 1){
			Console.WriteLine(1);
			return;
		}
		
		var di = PrimDec(P);
		long ret = 1;
		foreach(var k in di.Keys){
			long c = di[k] / N;
			for(int i=0;i<c;i++) ret *= k;
		}
		Console.WriteLine(ret);
		
		
	}
	long N,P;
	public Sol(){
		var d = rla();
		N = d[0]; P = d[1];
	}
	Dictionary<long,long> PrimDec(long A){
	 	Dictionary<long,long> D=new Dictionary<long,long>();
	 	if(A==1)return null;
	 	long rem=A;
	 	for(long i=2;i*i<=A;i++){
	 		if(rem%i==0){
	 			long cnt=0;
	 			while(rem%i==0){cnt++;rem/=i;}
	 			D.Add(i,cnt);
	 		}
	 		if(rem==1)break;
	 	}
	 	if(rem!=1)D.Add(rem,1);
	 	return D;
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}