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;
using System.Linq;
 
static class MainClass {
 
  public struct City{
    public long num;
    public City(long n){
      num = n;
    }
 
  }
 
  public static void Main (string[] args) {
    var temp = Console.ReadLine().Split(' ');
    var A = int.Parse(temp.ElementAt(0));
    var B = int.Parse(temp.ElementAt(1));
    var K = int.Parse(temp.ElementAt(2));
    var ans = 0;
    for(var i = Math.Min(A, B); i >= 1; i--){
      ans += A % i == 0 && B % i == 0 ? 1 : 0;
      if(ans == K) {
        ans = i;
        break;
      }
    }
    
    Console.WriteLine(ans);
  }
  public static long Euclidean(long a, long b){
    if(a % b == 0){return b;}
    return Euclidean(b, a % b);
  }
}