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, min, i;

  scanf("%d %d %d", &a, &b, &k);

  if (a > b) {
    max = a;
    min = b;
  }else {
    max = b;
    min = a;
  }

  for (i = min; i > 0; i--) {
    if (max % i == 0 && min % i == 0) {
      k--;
    }
    if (k == 0) {
      printf("%d\n", i);
      break;
    }
  }

  return 0;
}