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# (.NET Core 3.1.201) (judge verdict: Accepted)

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


class Program
{
    static void Main(string[] args)
    {
        // 入力
        //var s = Console.ReadLine();
        //var n = int.Parse(Console.ReadLine());
        long[] np = Console.ReadLine().Split().Select(long.Parse).ToArray();
        var n = np[0];
        var p = np[1];
        long ans = 1;

        var dic = prime_factorize(p);
        foreach (var item in dic)
        {
            for (int j = 0; j < item.Value / n; j++)
            {
                ans *= item.Key;
            }
        }


        // 出力
        Console.WriteLine(ans);
    }


    //素因数分解(ペア作成)
    public static Dictionary<long, long> prime_factorize(long n)
    {
        var res = new Dictionary<long, long>();
        for (long p = 2; p * p <= n; p++)
        {
            if (n % p != 0) continue;
            long num = 0;
            while (n % p == 0)
            {
                num++;
                n /= p;
            }
            res.Add(p, num);
        }
        if (n != 1) res.Add(n, 1);
        return res;
    }
}