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.Linq;
using System.Collections.Generic;

public class Hello
{
    public static void Main()
    {
        
        int[] a = Console.ReadLine().Split(' ').Select(x => int.Parse(x)).ToArray();
        int A = a[0];
        int B = a[1];
        int K = a[2];
        var list1 = new List<int>();
        var list2 = new List<int>();
        for(int i = 1; i <= A; i++)
        {
            if(A % i == 0)
            {
                list1.Add(i);
            }
        }
        
        for(int i = 0; i < list1.Count; i++)
        {
            if(B % list1[i] == 0)
            {
                list2.Add(list1[i]);
            }
        }
        
        list2.Sort();
        Console.WriteLine(list2[list2.Count - K]);
    }
}