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.Collections.Generic;
using System.Linq;
class Program
{
  static void Main(string[] args)
  {
    var a = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    var n = a[0];
    var p = a[1];

    List<long> yakuList = new List<long>();
    while (p % 2 == 0)
    {
      p /= 2;
      yakuList.Add(2);
    }

    while (true)
    {
      var b = IsPrime(p);
      if (b.IsPrime)
      {
        yakuList.Add(b.Num);
        break;
      }
      while (p % b.Num == 0)
      {
        p /= b.Num;
        yakuList.Add(b.Num);
      }
    }
    var aa = yakuList.GroupBy(x => x);

    long ans = 1;
    foreach (var j in aa)
    {
      ans *= (long)Math.Pow(j.Key, (long)(j.Count() / n));
    }
    Console.WriteLine(ans);
  }

  public static IsPrimeClass IsPrime(long num)
  {
    if (num < 2) return new IsPrimeClass()
    {
      IsPrime = true,
      Num = num
    };

    double sqrtNum = Math.Sqrt(num);
    for (int i = 3; i <= sqrtNum; i += 2)
    {
      if (num % i == 0)
      {
        return new IsPrimeClass()
        {
          IsPrime = false,
          Num = i
        };
      }
    }
    // 素数である
    return new IsPrimeClass()
    {
      IsPrime = true,
      Num = num
    };
  }
}
public class IsPrimeClass
{
  public bool IsPrime;
  public long Num;

}