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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.util.*;

public class Main{
        public static void main(String[] args){
                Scanner scan = new Scanner(System.in);
                int cntA = scan.nextInt();
                int cntB = scan.nextInt();
                int cntK = scan.nextInt();
                int tmp = 0;
                int count =0;

                if(cntA<cntB){
                        tmp = cntA;
                }else{
                        tmp = cntB;
                }

                for(int i=tmp ; i>1 ; i--){
                        if(cntA%i==0 && cntB%i==0){
                                count += 1;
                                if(count==cntK){
                                        System.out.println(i);
                                }
                        }
                }
        }
}