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 AtCoder20190303_B
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
            int m, n;
            if (input[0] > input[1])
            {
                m = input[0];
                n = input[1];
            }
            else
            {
                m = input[1];
                n = input[0];
            }

            int modded = int.MaxValue;
            var kouyakuNums = new List<int>();

            while (modded != 0)
            {
                modded = m % n;
                m = n;
                n = modded;
            }

            kouyakuNums.Add(1);
            for (int i = 2; i <= m / 2; i++)
            {
                if (m % i == 0)
                {
                    kouyakuNums.Add(i);
                }
            }
            kouyakuNums.Add(m);
            kouyakuNums.Reverse();
            Console.WriteLine(kouyakuNums[input[2] - 1]);
        }
    }
}