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>
#define MAX 101

int main(void)
{
  int a, b, k, x[MAX], y[MAX], v[MAX], p, q, m, c;
  int i, j = 0, l = 0;
  
  scanf("%d %d %d", &a, &b, &k);
  
  for(i = 1 ; i <= 50 ; i++)
  {
    if(a % i == 0)
    {
      x[j] = i;
      j++;
    }
    if(b % i == 0)
    {
      y[l] = i;
      l++;
    }
  }

  i = 1;
  p = j;
  q = l;
  for(j = 0 ; j < p ; j++)
  {
    for(l = 0 ; l < q ; l++)
    {
      if(y[l] == x[j])
      {
        v[i] = x[j];
        i++;
      }
    }
  }
  
  c = i - k;
  printf("%d", v[c]);
  
  return 0;
}