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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Atcoder
{

    class Program
    {
        static void Main(string[] args)
        {
            //素因数分解が必要
            var read = Console.ReadLine();
            long N = long.Parse(read.Split(' ')[0]);
            long P = long.Parse(read.Split(' ')[1]);
            long output = 1;
            if (N == 1)
            {
                Console.WriteLine(P);
                return;
            }
            for (int i = 2; i <= Math.Sqrt(P); i++)
            {
                int wareta = 0;
                while (P % i == 0)
                {
                    wareta++;
                    P = P / i;
                }
                if (wareta / N >= 1)
                {
                    output *= i;
                    output *= wareta;
                    output /= N;
                }
            }
            Console.WriteLine(output);
            return;
        }
    }
}