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>
#include <stdlib.h>
#include <float.h>

#define _max(_x, _y) ((_x)>(_y)?(_x):(_y))
#define _min(_x, _y) ((_x)>(_y)?(_y):(_x))

int main(void)
{
  int A,B,K, i, start;
  int count=0;

  scanf("%d %d %d", &A,&B,&K);
  start = _max(A,B);
  for (i=start; i>0; --i) {
    if ((A%i==0) && (B%i==0)) {
      ++count;
      if (count == K) {
        printf("%d\n", i);
        break;
      }
    }
  }  
  return 0;
}