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: Wrong Answer)

using System;

namespace ConsoleApp3
{
    class Program
    {
        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]);

            int counter = 0;
            for(int i=1;i<=100;i++)
            {
                if (A % i == 0 && B % i ==0)
                {
                    counter++;

                    if(counter == K)
                    {
                        Console.WriteLine(i.ToString());
                        return;
                    }
                }
            }

            //Console.ReadKey();
        }

    }
}