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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <stdio.h>

int main(void)
{
  int a,b,k,d;
  int c[100];
  
  c[0] = 1;
  
  scanf("%d",&a);
  scanf("%d",&b);
  scanf("%d",&k);
  
  int i;
  int count = 1;
  if(a >= b)
    d = a;
  else
    d = b;
  
  for(i = 2; i <= d; i++){
    if(a%i==0&&b%i==0){
      c[count] = i;
      count += 1;
    }
  }
  
  printf("%d",c[k-1]);
  
  return 0;
  
}