Problem:
Score : 200 points

Problem Statement

You are given positive integers A and B.

Find the K-th largest positive integer that divides both A and B.

The input guarantees that there exists such a number.

Constraints

All values in input are integers.

1 \leq A, B \leq 100

The K-th largest positive integer that divides both A and B exists.

K \geq 1

Input

Input is given from Standard Input in the following format:

A B K

Output

Print the K-th largest positive integer that divides both A and B.

Sample Input 1

8 12 2

Sample Output 1

2

Three positive integers divides both 8 and 12: 1, 2 and 4.
Among them, the second largest is 2.

Sample Input 2

100 50 4

Sample Output 2

5

Sample Input 3

1 1 1

Sample Output 3

1

Solution in C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Text;
using System.Numerics;
using System.IO;

namespace SolutionCS
{
    class Program
    {
        public static List<int> PrimeFactors(int n)
        {
            int i = 2;
            List<int> result = new List<int>();

            result.Add(1);
            while (i * i <= n)
            {
                if (n % i == 0)
                {
                    n /= i;
                    result.Add(i);
                }
                else
                {
                    i++;
                }
            }

            if (n != 1)
            {
                result.Add(n);
            }

            return result;
        }


        static void Main(string[] args)
        {
            string[] s = Console.ReadLine().Split(' ');
            int A = int.Parse(s[0]);
            int B = int.Parse(s[1]);
            int K = int.Parse(s[2]);

            List<int> p0 = PrimeFactors(A);
            List<int> p1 = PrimeFactors(B);
            List<int> comm = new List<int>();

            foreach(int i0 in p0)
            {
                foreach(int i1 in p1)
                {
                    if( i1 == i0)
                    {
                        comm.Add(i1);
                    }
                }
            }

            comm.Sort();

            Console.WriteLine(comm[K-1]);
        }
    }
}