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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;

class Main{
  static int gcd(int c,int d){
    while(true){
      int f=c%d;
      if(f==0){
        return d;
      }
      c=d;
      d=f;
    }
  }
  static ArrayList<Integer> divList(int n){
    ArrayList<Integer> div=new ArrayList<Integer>();
    for(int i=1;i*i<=n;i++){
      if(n%i==0){
        div.add(i);
        if(i*i!=n){
          div.add((int)(n/i));
        }
      }
    }
    return div;
  }
  public static void main(String[] args){
    Scanner sc=new Scanner(System.in);
    int a=sc.nextInt();
    int b=sc.nextInt();
    int c=gcd(a,b);
    List<Integer> l=divList(c);
    Collections.sort(l);
    System.out.println(l.get(l.size()-sc.nextInt()));
  }
}