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: Accepted)

#include <stdio.h>
int main(void)
{
  int a,b,k,max,ans,count,i;
  ans = 0;
  count =0;
  scanf("%d",&a);	
  scanf("%d",&b);	
  scanf("%d",&k);	
  max = a;
  if (b>a)	max = b;
  i = max;
  do {
	if (a % i==0 && b % i ==0)
		count = count + 1, ans = i;
	i = i -1;

  } while (count<k);
  printf("%d",ans);
  return 0;
}