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: Time Limit Exceeded)

using System;
using System.IO;

class Program
{
    static void Main()
    {
        string[] Input = Console.ReadLine().Split(' ');
        ulong N = ulong.Parse(Input[0]);
        ulong P = ulong.Parse(Input[1]);

        bool check = false;
        bool check2 = false;

        ulong cnt = 0;
        ulong cnt2 = 0;
        //答え
        ulong Answer = 0;
        

        while (check == false)
        {
            ulong Ptmp = P;

            cnt++;
            ulong Ncount = 0;

            for (ulong i = 0; i < N; i++)
            {
                cnt2 = cnt;
                if (Ptmp % cnt == 0)   //余りが存在しない、割り切れるとき
                {
                    Ptmp /= cnt;
                    Ncount++;
                    if (Ncount == N)
                    {
                        Answer = cnt;
                    }//N乗を因数にもってたら答えに含める
                }
                else
                //余りが存在する、割り切れないとき
                {
/*                    for (ulong j = 0; j < N; j++)
                    {
                        if (P < cnt2)
                        {
                            check = true;
//                            check2 = true;
                            break;
                            
                        }
                        cnt2 *= cnt2;
                    }

                    if (check2 == true)
                    {
                        check2 = false;
                        break;
                    }*/
                    ulong cnt3 = 1;
                    for (ulong j = 0; j < N; j++)
                    {
                        cnt3 *= cnt;
                        if (P < cnt3)
                        {
                            check = true;
                            break;
                        }
                    }
                    break;
                }
            }
        }

        Console.WriteLine(Answer);
    }
}