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;
using System.Threading.Tasks;

namespace ABC120_B
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] strs = Console.ReadLine().Split(' ');
            int a = int.Parse(strs[0]);
            int b = int.Parse(strs[1]);
            int k = int.Parse(strs[2]);

            int divAnsIndex = 0;

            int div = 100;

            if (a < b)
            {
                div = a;
            }
            else
            {
                div = b;
            }

            int i = div;
            for (; i >= 1; --i)
            {
                if (a % i == 0 && b % i == 0)
                {
                    divAnsIndex++;

                    if (divAnsIndex == k) break;
                }
            }

            Console.WriteLine("{0}", i);
        }
    }
}