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.Linq;
using static System.Math;
using System.Collections.Generic;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var n = long.Parse(line[0]);
        var p = long.Parse(line[1]);
        if (n == 1) { Console.WriteLine(p); goto exit; }
        if (p == 1) { Console.WriteLine(1); goto exit; }
        var rp = (int)Sqrt(p);
        var a = GeneratePrime(rp + 1);
        var ans = getAns(a, n, p);
        Console.WriteLine(ans);
        exit:;
    }
    static long getAns(List<int> a, long n, long p)
    {
        var ans = 1L;
        foreach (var x in a)
        {
            var count = 0;
            if (p < x) break;
            while (true)
                if (p % x == 0) { count++; p /= x; }
                else break;
            ans *= (long)Pow(x, count / n);
        }
        return ans;
    }
    public static List<int> GeneratePrime(int m)
    {
        var a = new List<int>();
        int p;
        var sqrtMax = Sqrt(m);
        var s = Enumerable.Range(2, m - 1).ToList();
        do
        {
            p = s.First();
            a.Add(p);
            s.RemoveAll(n => n % p == 0);
        }
        while (p < sqrtMax);
        a.AddRange(s);
        return a;
    }
}