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 (Clang 3.8.0) (judge verdict: Runtime Error)

#include <stdio.h>
int main(void){
    
int a,b,k,i,j;
int x,y;
int s[100];

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


    if(a>b){
        for(i=1; i<b; i++){
            if(b%i==0 && a%i==0){
            s[j]=i;
            j++;
            
            }
        }
    }
    else if(b>a){
        for(i=1; i<a; i++){
            if(b%i==0 && a%i==0){
            s[j]=i;
            j++;
            
            }
        }
    }

printf("%d",s[k]);
}