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.IO;

class Program
{
    static long answer = 1;

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

        long i = 2;
        long tmp = P;
        long count = 0;

//        Console.WriteLine(answer);

        while (i * i <= P) //※i <= √P
        {
            if (tmp % i == 0)
            {
//                Console.WriteLine(answer);

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

        if (tmp != 1)
        {
            count++;
            if (count == N) answer *= tmp;
        }

        Console.WriteLine(answer);
    }


}