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 Caddi2018
{
    class Program
    {
        static void Main(string[] args)
        {
            var obj = new Q3();
            obj.Solver();
        }
    }
    class Q3
    {

        public void Solver()
        {
            var buf = Console.ReadLine().Split().Select(long.Parse).ToArray();

            long N = buf[0];
            long P = buf[1];

            long remain = P;
            long i = 2;
            long answer = 1;
            long count = 0;
            while (i <= remain)
            {
                if (remain % i == 0)
                {
                    count++;
                    remain /= i;

                    if (count == N)
                    {
                        answer *= i;
                        count = 0;
                    }
                }
                else
                {
                    i++;
                }
            }

            Console.WriteLine(answer);

        }
    }

    //class Q2
    //{

    //    class AB
    //    {
    //        public int A { get; set; }
    //        public int B { get; set; }
    //    }
    //    public void Solver()
    //    {
    //        var buf = Console.ReadLine().Split().Select(int.Parse).ToArray();

    //        var N = buf[0];
    //        var H = buf[1];
    //        var W = buf[2];

    //        var AB = new List<AB>();
    //        for (int i = 0; i < N; i++)
    //        {
    //            buf = Console.ReadLine().Split().Select(int.Parse).ToArray();
    //            AB.Add(new AB { A = buf[0], B = buf[1] });
    //        }

    //        var count = AB.Count(x => x.A >= H && x.B >= W);
    //        Console.WriteLine(count);

    //    }
    //}

    //class Q1
    //{
    //    public void Solver()
    //    {
    //        var str = Console.ReadLine();

    //        Console.WriteLine(str.Count(s => s == '2'));

    //    }
    //}
}