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.Collections.Generic;
using System.Linq;

namespace CFBC
{
    static class MainClass
    {

        public static void Main(string[] args)
        {


            string[] input1 = Console.ReadLine().Split(' ');
            long N = long.Parse(input1[0]);
            long P = long.Parse(input1[1]);

            if(P==1 || N ==1){
                Console.WriteLine(P);
                return;

            }

            List<long>pf = PF(P).ToList();
            pf.Sort();

            if(N>pf.Count()){
                N = pf.Count();
            }



            long tmp = 0;
            int tmp2 = 0;
            int cnt = pf.Count();
            for (int i = 0; i < cnt - N; i++){
                tmp2 = cnt - 2*i-1;
                if(tmp2<0){
                    tmp2 = 1;
                }
                if(pf[tmp2] % pf[0] ==0 && (tmp2 -1 >0)){
                    tmp2 = tmp2 - 1;
                }
                tmp = pf[0] * pf[tmp2];
                pf[tmp2] = tmp;
                pf.RemoveAt(0);
            }

        

            long ans = 0;
            if (pf.Count() == 1)
            {
                ans = pf[0];
            }
            else
            {
                for (int j = 0; j < pf.Count() - 1; j++)
                {
                    ans = Gcd(pf[j], pf[j + 1]);
                }
            }
           

            Console.WriteLine(ans);

            return;


        }



        public static long Gcd(long a, long b)
        {
            long tmp;
            // a<bにする
            if (a >= b)
            {
                tmp = a;
                a = b;
                b = tmp;
            }

            if (a == 0)
            {
                return b;
            }

            tmp = a;
            a = b % a;
            b = tmp;
            return Gcd(a, b);

        }


        public static IEnumerable<long> PF(long n)
        {
            long i = 2;
            long tmp = n;

            while (i * i <= n) //※1
            {
                if (tmp % i == 0)
                {
                    tmp /= i;
                    yield return i;
                }
                else
                {
                    i++;
                }
            }
            if (tmp != 1) yield return tmp;//最後の素数も返す
        }




    }

}