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: Accepted)

#include<bits/stdc++.h>
using namespace std;
int d[100];

int main()
{
    int a,b,k;
    cin >> a >> b >> k;

 for(int i = 1; i <= sqrt(a); i++){
        if(a % i == 0){
            if(a/i == i){
                d[i]++;
            }
            else{
                d[i]++;
                d[a/i]++;
            }
        }
    }

     for(int i = 1; i <= sqrt(b); i++){
        if(b % i == 0){
            if(b/i == i){
                d[i]++;
            }
            else{
                d[i]++;
                d[b/i]++;
            }
        }
    }

    int n = min(a,b);
    vector<int>v;
    for(int i = n; i >= 0; i--){
        if(d[i] >= 2){
            v.push_back(i);
        }
    }

    cout << v[k-1]<<endl;
    return 0;
}