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.Collections.Generic;
using System.Linq;
class Program{
	static void Main(){
		long[] s=Array.ConvertAll(Console.ReadLine().Split(),long.Parse);
		var hs=new Dictionary<long,int>();
		long ans=1;
		double r=Math.Sqrt(s[1]);
		for(long i=2;i<=r;i++){
			if(s[1]%i==0){
				s[1]/=i;
				if(hs.ContainsKey(i)){hs[i]++;}
				else{hs.Add(i,1);}
				i=1;
			}
		}
		foreach(KeyValuePair<long,int> e in hs){
			long q=e.Value;
			while(q>=s[0]){
				ans*=e.Key;
				q-=s[0];
			}
		}
		Console.WriteLine(ans);
	}
}