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;
    scanf("%d %d %d",&a,&b,&k);
    int A[a];
    int n = -1;
    for(int i = 1; i <= a; i++){
        if(a % i == 0){
            n++;
            A[n] = i;
            
        }
    }
    int i = n;
    int count = 0;
    int num = 0;
    while(1){
        if(b % A[i] == 0){
            
            num = A[i];
            count++;
        }
        i--;
        if(count == k) break;
    }
    printf("%d",num);
    return 0;
}