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# (.NET Core 3.1.201) (judge verdict: Accepted)

using System;
using System.Linq;

class Program
{
    static void Main()
    {
        var input = Console.ReadLine().Split().Select(int.Parse).ToArray();
        var A = input[0];
        var B = input[1];
        var K = input[2];

        var result = 0;
        var r = 0;
        for (var i = Math.Min(A, B); ; i--)
        {
            if (A % i == 0 && B % i == 0)
            {
                r++;
                if (K == r)
                {
                    result = i;
                    break;
                }
            }
        }
        Console.WriteLine(result);
    }
}