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: Accepted)

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

namespace CompetitiveProgramming
{
    class Program
    {
        static void Main(string[] args)
        {
            MainStream();
        }

        static void MainStream()
        {
            var array = new List<int>();
            string[] a_b_k = Console.ReadLine().Split(' ');
            int a = int.Parse(a_b_k[0]);
            int b = int.Parse(a_b_k[1]);
            int k = int.Parse(a_b_k[2]);

            for(var i=1;i<=a;i++)
            {
                if(a%i==0 && b%i==0)
                {
                    array.Add(i);
                }
            }

            Console.WriteLine(array[array.Count - k]);
        }



    }
}