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: Wrong Answer)

import java.util.*;
import java.io.*;
class Program{

}
class Main{
    public static void main(String args[]) throws IOException{
    BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
    Scanner sc = new Scanner(System.in);
    int A = sc.nextInt(), B = sc.nextInt(), K = sc.nextInt();
    int small = Math.min(A,B), big = Math.max(A,B);
    ArrayList <Integer> fact = new ArrayList<Integer>();
    for(int i = 1;i<=(int)Math.sqrt(small);i++){
        if (small%i==0){
            if(big%i==0){
                fact.add(i);
            }
                if (big%(small/i)==0) fact.add(small/i);
            
        }
    }
    Collections.sort(fact);
    //System.out.println(fact);
    System.out.println(fact.get(K-1));
    }
}