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: Wrong Answer)

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

namespace CADDiC
{
    class Program
    {
        static long N;
        static void Main(string[] args)
        {
            //Console.WriteLine("Hello World!");
            var NP = Console.ReadLine().Split().Select(long.Parse).ToArray();
            N = NP[0];
            var P = NP[1];

            if (P == 1) { Console.WriteLine(1); Console.ReadKey(); return; }

            //List<long> primeNumber = GeneratePrime(P);
            long last = 0;
            long count = 1;
            long ans = 1;
            foreach (long f in Factoring(P)){
                if (last == f)
                {
                    count++;

                    if (count >= N)
                    {
                        ans *= f;
                        count = long.MinValue;
                        continue;
                    }
                }
                else count = 1;
                last = f;
            }
            
            Console.WriteLine(ans);
            Console.Read();
        }

        private static long HowManyTimesCanDivision(long P, long division)
        {
            if (P % division != 0) return 0;
            return 1 + HowManyTimesCanDivision(P / division, division);
        }

        static IEnumerable<long> Factoring(long number)
        {
            if (number == 1)
                yield break;
            // 最小の素数をリストに
            var primes = new List<long>() { 2 };
            var tmp = number;
            // 割れなくなったらやめる
            
            while (tmp != 1)
            {
                foreach (var prime in primes)
                {
                    // 剰余が発生するまで割り続けて、終わったら次の素数に
                    while (tmp % prime == 0)
                    {
                        tmp = tmp / prime;
                        yield return prime;
                    }
                }
                if (tmp == 1)
                    // 割れなくなったらやめる
                    yield break;
                var maxPrime = primes.Max();
                if (Math.Sqrt(tmp) < maxPrime)
                {
                    // 最大の素数が残っている数の平方より大きいなら残っている数は素数
                    primes.Add(tmp);
                    continue;
                }
                // 次の素数を求める
                primes.Add(LongRange(maxPrime, tmp - maxPrime)
                    .First(s1 => !primes.Any(s2 => s1 % s2 == 0)));
            }
        }

        static IEnumerable<long> LongRange(long startNum, long count)
        {
            for (var i = startNum; i < startNum + count; i++)
                yield return i;
        }
    }
}