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.Diagnostics;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main()
    {
        string[] s = Console.ReadLine().Split();
        long n = long.Parse(s[0]);
        long p = long.Parse(s[1]);

        if (n == 1)
        {
            Console.WriteLine(p);
            return;
        }

        long ans = 1;

        for (long i = (long)Math.Sqrt(p); 2 <= i; i--)
        {
            if (p % Math.Pow(i, n) == 0)
            {
                ans = i;
                break;
            }
        }
        Console.WriteLine(ans);
    }
}