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: Accepted)

using System;
using System.Linq;

namespace CADDi2018
{
    class C
    {
        static void Main(string[] args)
        {
            //input
            long[] input = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long N = input[0];
            long P = input[1];

            if (N == 1) { Console.WriteLine(P); return; }

            long[] Array = new long[(int)Math.Ceiling(Math.Sqrt(P))];
            long p = P;
            long res = 1;
            for (int i = 2; i < Math.Sqrt(P); i++)
            {
                //素因数分解
                while (p % i == 0)
                {
                    Array[i]++;
                    p /= i;
                }
                Array[i] /= N;
                res *= (long)Math.Pow(i, Array[i]);
            }

            //Console.WriteLine(string.Join(",", Array));
            Console.WriteLine(res);
        }
    }
}