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,i,a,b,x,y;

  scanf("%d%d%d",&A,&B,&K);

  a = 0;
  b = 0;
  if (A > B){
    a = B;
  }
  else {
    a = A;
  }
  for (i=a;b<K;i--){
    x = A % i;
    y = B % i;
    if (x==0 && y==0){
      b++;
    }
  }
  printf("%d\n",i+1);
  return 0;
}