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: Runtime Error)

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

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayLong();
            var N = input[0];
            var P = input[1];
            var list = PrimeList(100000);
            var num = 0;
            var cnt = 0L;
            var lcnt = 0L;
            var ans = 1L;
            while (P != 1)
            {
                if (P % list[num] == 0)
                {
                    P /= list[num];
                    cnt++;
                    lcnt++;
                }
                else
                {
                    if (cnt >= N)
                    {
                        ans *= cnt / N * list[num];
                    }
                    num++;
                    cnt = 0;
                }
            }
            if (cnt >= N)
            {
                ans *= cnt / N * list[num];
            }
            if (lcnt < N) { Console.WriteLine(1); return; }

            Console.WriteLine(ans);
            Console.ReadLine();
        }

        static List<int> PrimeList(long num)
        {
            var pri = new List<int>();
            pri.Add(2);

            for (var i = 3; i <= num; i += 2)
            {
                var prime = true;
                for (var j = 3; j <= Math.Sqrt(i); j += 2)
                {
                    if (i % j == 0)
                    {
                        prime = false;
                        break;
                    }
                }
                if (prime) pri.Add(i);
            }

            return pri;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}