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: Time Limit Exceeded)

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

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            var l = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long N = l[0], P = l[1];

            var prime = PrimeFactorsDictionary(P);
            var ans = 1L;
            foreach (var p in prime)
            {
                for (var i = 0; i < p.Value / N; i++)
                    ans *= p.Key;
            }

            Console.WriteLine(ans);
        }


        public static Dictionary<long, int> PrimeFactorsDictionary(long n)
        {
            var i = 2;
            var tmp = n;
            var dict = new Dictionary<long, int>();

            while (i * i <= n)
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    if (dict.ContainsKey(i))
                        dict[i]++;
                    else
                        dict[i] = 1;
                }
                else
                {
                    i++;
                }

                if (tmp == 1) return dict;
            }

            if (tmp != 1)
                dict[tmp] = 1;

            return dict;
        }
    }
}