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 Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.*;
import java.util.*;
import java.util.ArrayList;
import java.util.Iterator;
import java.util.List;
import java.util.Collections;
import java.util.Arrays;

public class Main {
	public static void main(final String[] args){
    
    final Scanner sc = new Scanner(System.in);
    //final List<Integer> list = new ArrayList<>();
    //final List<Integer> list2 = new ArrayList<>();
    //final List<Long> list3 = new ArrayList<>();

    int a = sc.nextInt();
    int b = sc.nextInt();
    int k = sc.nextInt();
    int count = 0;
    int high = 0;
    if(a >= b){
        high = a;
    }else{
        high = b;
    }

    for(int i = high; i > 0 ; i--){
        if(a % i == 0 && b % i == 0){
            count++;
        }
        if(k == count){
            System.out.println(i);
            System.exit(0);
        }
    }

    




    







}
}