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: Time Limit Exceeded)

using System;
using System.IO;

class Program
{
    static void Main()
    {
        string[] Input = Console.ReadLine().Split(' ');
        long N = long.Parse(Input[0]);
        long P = long.Parse(Input[1]);

        bool check = false;
        long cnt = 0;
        long Answer = 0;
        

        while (check == false)
        {
            long Ptmp = P;

            cnt++;
            long Ncount = 0;
            for (int i = 0; i < N; i++)
            {
                if (Ptmp % cnt == 0)   //余りが存在しない、割り切れるとき
                {
                    Ptmp /= cnt;
                    Ncount++;
                    if (Ncount == N) Answer = cnt;  //N乗を因数にもってたら答えに含める
                }
                else
                {
                    if (P < Math.Pow(cnt, N))
                    {
                        check = true;
                    }
                    break;
                }
            }
        }

        Console.WriteLine(Answer);
    }
}