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;
using System.Text;

namespace ConsoleApp3
{
    class Program
    {
        static void Main(string[] args)
        {
            Main main = new Main();
            main.Calc();
        }
    }
    class Main { 

        public void Calc()
        {
            var input = Console.ReadLine().Split().Select(int.Parse).ToList();
            var A = input[0];
            var B = input[1];
            var K = input[2];
            var cnt = 0;
            var ans = 0;
            for(var i = 1000;0 < i; i--)
            {
                if(A % i == 0 && B % i == 0)
                {
                    cnt++;
                    if (cnt == K)
                    {
                        ans = i;
                        break;
                    }
                }
            }
            Console.WriteLine(ans);
            Console.ReadLine();
        }
    }
}