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.Linq;
using System.Collections.Generic;

namespace CADDiC2
{
    class Program
    {
        static long N;
        static void Main(string[] args)
        {
            var NP = Console.ReadLine().Split().Select(long.Parse).ToArray();
            N = NP[0];
            var P = NP[1];

            if (P == 1) { Console.WriteLine(1); Console.ReadKey(); return; }

            List<long> primeNumber = GeneratePrime(P);

            long ans = 1;
            foreach (var p in primeNumber)
            {
                long count = HowManyTimesCanDivision(P, p);
                if (count >= N) ans *= p;
            }

            Console.WriteLine(ans);
            Console.ReadKey();
        }

        private static long HowManyTimesCanDivision(long P, long division)
        {
            if (P % division != 0) return 0;
            return 1 + HowManyTimesCanDivision(P / division, division);
        }

        public static List<long> GeneratePrime(long max)
        {
            System.Diagnostics.Debug.Assert(max >= 2);  // maxは2以上の数

            long prime = 0;
            double sqrtMax = Math.Pow(max, 1.0 / N);
            var primeList = new List<long>();
            
            var searchList = new List<long>();
            for (long i = 2; i < (long)sqrtMax + 1; i++)
            {
                searchList.Add(i);
            }

            while (searchList.Count > 0)
            {
                prime = searchList.First();
                primeList.Add(prime);
                searchList.RemoveAll(n => n % prime == 0);
                
            }
            
            primeList.AddRange(searchList);

            return primeList;
        }
    }
}