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)

// デバッグ実行：Ctrl+F5

using System;
using System.Collections.Generic;
using System.Linq;
class Program
{

    static void Main(string[] args)
    {
        String line;
        line = Console.ReadLine();
        String[] words = line.Split(' ');

        long A = long.Parse(words[0]);
        int N;
        if (A > int.MaxValue) N = int.MaxValue;
        else N = (int)A;
        long P = long.Parse(words[1]);
        if (N == 1)
        {
            Console.WriteLine(P);
            return;
        }

        var yakusu = Soinsu(P, N).ToList();
        yakusu.Sort();
        long Kouyakusu = 1;
        if (N > int.MaxValue) N = int.MaxValue;
        for (int i = 0; i < yakusu.Count - N + 1; i++)
        {
            var kouho = yakusu[i];
            var OK = true; // 約数としてOKかどうか
            for (int j = i + 1; j < i + N; j++)
            {
                if (kouho != yakusu[j])
                {
                    OK = false;
                    i = j - 1;
                    break;
                }
            }
            if (OK)
            {
                Kouyakusu *= kouho;
                i = i + N - 1;
            }
        }

        Console.WriteLine(Kouyakusu);
    }

    static IEnumerable<long> Soinsu(long N, int kaisu)
    {
        long j = 2;
        long now = N;
        long limit = N;
        int keisan_limit = (int)Math.Sqrt(kaisu) + 1;
        for (int i = 0; i < keisan_limit - 1; i++)
        {
            limit = (long)Math.Sqrt(limit) + 1;
            if (limit <= 3) break;
        }
        while (j <= limit)
        {
            if (now % j == 0)
            {
                now /= j;
                yield return j;
            }
            else
            {
                j++;
            }
        }
    }
    //static IEnumerable<long> Soinsu(long N, List<long> SosuList)
    //{
    //    int i = 0;
    //    long now = N;
    //    while (true)
    //    {
    //        if (i >= SosuList.Count) break;
    //        if (SosuList[i] > N) break;
    //        if (now % SosuList[i] == 0)
    //        {
    //            now /= SosuList[i];
    //            yield return SosuList[i];
    //        }
    //        else
    //        {
    //            i++;
    //        }
    //    }
    //}

    //static List<long> MakeSosuList(long N, int kaisu)
    //{
    //    var list = new List<long>();
    //    if (N < 2)
    //    {
    //        return list;
    //    }

    //    long limit = N;
    //    int keisan_limit = (int)Math.Sqrt(kaisu) + 1;
    //    for (int i = 0; i < keisan_limit - 1; i++)
    //    {
    //        limit = (long)Math.Sqrt(limit) + 1;
    //        if (limit <= 3) break;
    //    }
    //    for(long i = 2; i < limit; i++)
    //    {
    //        var OK = true;
    //        foreach(long sosu in list)
    //        {
    //            if (i % sosu == 0)
    //            {
    //                OK = false;
    //                break;
    //            }
    //        }
    //        if (!OK) continue;
    //        list.Add(i);
    //    }
    //    return list;
    //}
}