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;

public class AtCoder
{
    public static void Main()
    {
        string[] s;
        s = NextS();

        long n, p;
        n = long.Parse(s[0]);
        p = long.Parse(s[1]);
        //w = int.Parse(s[2]);
        long x = 1;
        long m = 2;
        long ans = 0;
        bool f1 = true;
        long y = 1;
        if (n == 1) Console.WriteLine(p);
        else if (n > 40) Console.WriteLine(1);
        else
        {
            while (f1)
            {
                for (int i = 1; i <= n; i++)
                {
                    x *= m;
                    if (x > p)
                    {
                        f1 = false;
                        break;
                    }
                }
                if (f1)
                {
                    m++;
                    x = 1;
                }
            }
            for (int i = 1; i <= m; i++)
            {
                y = (long)Math.Pow(i, n);
                if (p % y == 0) ans = i;
            }
            Console.WriteLine(ans);
        }
       
        
    }

    static void DebugWL(object x) { System.Diagnostics.Debug.WriteLine(x); }
    static string[] NextS() { return Console.ReadLine().Trim().Split(' '); }
}