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;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp111 {
    class Program {
        static void Main(string[] args)
        {
            string input = Console.ReadLine();

            List<int> inputInt = StringSplit(input);
            int A = inputInt[0];
            int B = inputInt[1];
            int K = inputInt[2];

            List<int> ans = new List<int>();

            for(int i = 1; i <= A; i++)
            {
                if(A % i == 0 && B % i == 0)
                {
                    ans.Add(i);
                }
            }
            Console.WriteLine(ans[K - 1]);
        }

        static List<int> StringSplit(string input)
        {
            string[] inputStr = input.Split(' ');
            int[] inputInt = new int[input.Length];
            List<int> inputList = new List<int>();

            foreach(string n in inputStr)
            {
                inputList.Add(int.Parse(n));
            }

            return inputList;
        }
        
    }
}