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, min;
  scanf("%d %d %d", &a, &b, &c);
  if(a < b){
    min = a;
  }
  else{
    min = b;
  }
  
  int i;
  int cnt = 0;
  for(i = min; min > 0; min--){
    if((a % i == 0) && (b % i == 0)){
      cnt++;
      if(cnt == c){
        printf("%d\n", i);
        break;
      }
    }
  }
  return 0;
}