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;

namespace _120_ABC
{
    class Program02
    {
        static void Main(string[] args)
        {
            string[] Input = Console.ReadLine().Split(' ');
            int A = int.Parse(Input[0]);
            int B = int.Parse(Input[1]);
            int K = int.Parse(Input[2]);

            var AnswerList = new List<int>();

            for(int i = 1; i <= 100; i++)
            {
                if(A % i == 0 && B % i == 0)
                {
                    AnswerList.Add(i);
                }
            }

            Console.WriteLine(AnswerList[AnswerList.Count-K]);

        }
    }
}