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;
using System.Threading.Tasks;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            var line = "4 972439611840".Split(' ');
            var N = Int64.Parse(line[0]);
            var P = Int64.Parse(line[1]);

            var a = primeFactorization(P);

            if (a.Count == 1)
            {
                Console.WriteLine(a[0]);
            }
            else
            {
                // Nよりa.Countが大きい
                var newA = getA(a, N);


                Console.WriteLine(newA[0]);

            }


        }


        static List<long> primeFactorization(long n)
        {
            var result = new List<long>();
            if (n == 1) return new List<long> { 1 };

            var m = 2;
            while(n > 1)
            {
                while (n % m==0)
                {
                    result.Add(m);
                    n = n / m;
                }
                m++;
            }

            return result;
        }

        static List<long> getA(List<long> a, long N)
        {
            if (a.Count == N) return a;

            var deleteItems = new List<long>();

            a.Sort();
            for(var i = a.Count; i > N; i--)
            {
                var a1 = a[a.Count - 1];
                var a2 = a[a.Count - 2];
                deleteItems.Add(a1);
                deleteItems.Add(a2);
                a.Add(a1*a2);
            }

            foreach(var deleteItem in deleteItems)
            {
                a.Remove(deleteItem);
            }
            return a;
        }
    }

}