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: Runtime Error)

#include <stdio.h>

int main(){
    int a,b,c;
    int i = 51, count = 0;

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

    while(1){
        i--;
        if(a % i == 0 && b % i == 0){
            count++;
        }
        if(count == c){
            break;
        }
      	else if(i < 0){
        	break;
        }
    }
    printf("%d\n" ,i);

    return 0;  
}