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;
using System.Text;

namespace AtCorder
{
	public class Program
	{
		static void Main(string[] args)
		{
			var np = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
			long n = np[0];
			long p = np[1];

			var primes = Primes(p);
			var values = primes.Where(x => x.Value >= n).ToArray();
			long ans = 1;
			for (long i = 0; i < values.Length; i++) {
				ans *= values[i].Key * (values[i].Value / n);
			}

			Console.WriteLine(ans);
		}

		static Dictionary<long, long> Primes(long n)
		{
			long max = (long)Math.Ceiling(Math.Sqrt(n)) + 1;
			var dic = new Dictionary<long, long>();
			for (long i = 2; i < max; i++) {
				while (n % i == 0) {
					if (dic.ContainsKey(i) == false) {
						dic[i] = 1;
					} else {
						dic[i] += 1;
					}

					n /= i;
				}
			}

			if (n != 1) {
				dic[n] = 1;
			}

			return dic;
		}
	}
}