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;

namespace Main
{
    class Program
    {
        static void Main(string[] args)
        {
            var NP = Array.ConvertAll(Console.ReadLine().Split(' '), long.Parse);
            long N = NP[0], P = NP[1];

            long max = (long)Math.Ceiling(Math.Pow(P, 1 / (double)N));
            long ans = 1;
            for(long i = max; i >= 1; i--)
            {
                if (N % i != 0)
                    continue;
                long tmpans = 1;
                for (int j = 0; j < N; j++)
                    tmpans *= i;
                if (P % tmpans == 0)
                {
                    ans = i;
                    break;
                }
            }

            Console.WriteLine(ans);
        }
    }
}