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


class maki {
    static void Main(string[] args) {
        int[] cin=Console.ReadLine().Split().Select(int.Parse).ToArray();
        //int n = int.Parse(Console.ReadLine());
        //string s=Console.ReadLine();
        int a=0;
        for(int i=100;i>=1;i--){
            if(cin[0]%i==0 && cin[1]%i==0){
                a++;
                if(a==cin[2]){
                    Console.WriteLine(i);
                    return;
                }
            }
        }
        
    }
}