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.*;
public class Main {

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int A =sc.nextInt();
		int B =sc.nextInt();
		int K =sc.nextInt();
		int count =0;
		if(A<B){
			for(int i=1;i<=A;i++) {
				if(A%i==0&&B%i==0) {
					count++;
					if(count==K){
						System.out.println(i);
					}
				}
			}
		}
		else if(A>B){
			for(int i=1;i<=B;i++) {
				if(A%i==0&&B%i==0) {
					count++;
					if(count==K){
						System.out.println(i);
					}
				}
			}
		}
		else if(A==B){
			for(int i=1;i<=B;i++) {
				if(A%i==0&&B%i==0) {
					count++;
					if(count==K){
						System.out.println(i);
					}
				}
			}
		}
	}
}