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;

class Program
{
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            long n = long.Parse(input[0]);
            long p = long.Parse(input[1]);

            long g = 1;
            long cnt = 0;

            for(long i = 2; i <= p; i++)
            {
                cnt = 0;

                while (true)
                {
                    if (p % i == 0)
                    {
                        p /= i;
                        cnt++;
                        if(cnt == n)
                            g *= i;
                    }
                    else
                        break;
                }

            }

            Console.WriteLine(g);
        }
}