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.*;

class Main{
  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);
    int a,b,k,r,num;
    a = sc.nextInt();
    b = sc.nextInt();
    k = sc.nextInt();
    if(a==1&&b==1)
      System.out.println(1);
    if(a<b){
      num = a;
      a = b;
      b = num;
    }
    r = a%b;
    while(r!=0){
      a = b;
      b = r;
      r = a%b;
    }
    int x = 0,j = 1;
    for(int i=2;i<=b;i++){
      int c;
      c = b%i;
      if(c==0){
        j++;
        x = i;
        if(j==k){
          System.out.println(b/x);
          break;
        }
      }
    }
  }
}