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 C (Clang 3.8.0) (judge verdict: Wrong Answer)

#include<stdio.h>
int main(void){
  int a, b, c;
  scanf("%d %d %d", &a, &b, &c);
  
  int ans, i;
  int cnt = 1;
  int mae = 2;
  if(c == cnt){
    printf("%d\n", cnt);
    return 0;
  }
  
  for(i = 2; i <= 100; i++){
    ans = a % i;
    if(ans == 0){
      ans = b % i;
      if(ans == 0){
        cnt++;
        if(cnt == c){
          printf("%d\n", i);
          break;
        }
      }        
    }
  }
  return 0;
}