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(){
  int a,b,k;
  int i = 0;
  
  scanf("%d", &a);
  scanf("%d", &b);
  scanf("%d", &k);
  
  int n = 1;
  int count = 0;
  int answer;
  for(n=100;n>= 1;n--){
    if(a%n == 0 && b%n == 0){
      count++;
        if(count == k){
          answer = n;
        }
    }
  }
  printf("%d",answer);
  
return 0;  
}