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;
 
class Program {
	static void Main (string[] args) {
		string[] str = Console.ReadLine().Split(' ');
    	int a = int.Parse(str[0]);
    	int b = int.Parse(str[1]);
    	int k = int.Parse(str[2]);
    
    	int sml = (a > b) ? b : a;
    	List<int> nums = new List<int>();
    	for (int cnt = 1; cnt <= sml; cnt++) {
        	if (a % cnt == 0 && b % cnt == 0) {
            	nums.Add(cnt);
        	}
        }
    	int index = nums[nums.Count - k];
    	Console.WriteLine(index);
	}
}