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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include <algorithm>
#include <stdio.h>
#include <iostream>
#include <cstdlib>
#include <vector>
using namespace std;

int main(){
    int A, B, K,count=1,X[100];
    cin >> A >> B >> K;
    for(int i=1;i<=100;i++){
        if(A%i==0 && B%i==0){
        X[count] = i;
        count = count + 1;
        }
    }
    cout << X[K] << endl;
    return 0;
}