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: Wrong Answer)

#include<stdio.h>

int main(){
  
  int a,b,k,less;
  int count;
    
  scanf("%d%d%d",&a,&b,&k);
  
  if(a>=b)
    less=b;
  else
    less=a;
  
  count=0;
  
  for(int i=1;i<=less;i++){

  if(a%i==0 && b%i==0){
    count++;
  if(count>=k){
   printf("%d",i);
    break;
  }
  }
  }
  return 0;
}