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.Text;
using System.Linq;
using static MyIO;


public class C
{
	public static void Main()
	{
		long N = GetLong();
		long P = GetLong();
		
		List<int> primes = sieve((int)Math.Sqrt(P));

		var numFactor = new Dictionary<long, long>();
		long tmp = P;
		for(int i = 0; i < primes.Count; i++)
		{
			long prime = (long)primes[i];
			while(tmp % prime == 0)
			{
				tmp /= prime;
				long currentNum = 0;
				numFactor.TryGetValue(prime, out currentNum);
				numFactor[prime] = currentNum + 1;
			}
			if(tmp == 1)
				break;
		}
		if(tmp != 1)
			numFactor[tmp] = 1;

		long gcdMax = 1;
		foreach(var key in numFactor.Keys)
			for(long i = 0; i < numFactor[key] / N; i++)
				gcdMax *= key;
		Console.WriteLine(gcdMax);
	}

	private static List<int> sieve(int N)
	{
		List<int> primeList = new List<int>();
		bool[] isPrime = new bool[N+1];
		for(int i = 2; i <= N; i++)
			isPrime[i] = true;

		for(int i = 2; i <= N; i++)
		{
			if(isPrime[i])
			{
				primeList.Add(i);
				for(int j = 2 * i; j <= N; j += i)
					isPrime[j] = false;
			}
		}

		return primeList;
	}
}


public static class MyIO
{
	private static string[] args = null;
	private static int num = -1;
	private static int used = -1;

	private static string getArg()
	{
		if(used == num)
		{
			args = Console.ReadLine().Split(' ');
			num = args.Length;
			used = 0;
		}
		return args[used++];
	}

	public static int GetInt(){ return int.Parse(getArg()); }
	public static long GetLong(){ return long.Parse(getArg()); }
	public static double GetDouble(){ return double.Parse(getArg()); }
	public static string GetString(){ return getArg(); }
}