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>
#include <string.h>
int main(void){

  int A=0,B=0,K=0,ans=0,len;
  scanf("%d%d%d",&A,&B,&K);
  int num[100]={0};
  
  for(int i=1;i<=100;i++){
  	if(A%i == 0 && B%i == 0){
        num[i]=i;
       len=strlen(num);
    	if(len>K){
    		ans=num[i];
      		return 0;
   	  }
    }
  }
  
  printf("%d",ans);


 return 0;
}