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 main(){
int a,b,k,data[200]={0},j=1;
cin >> a >> b >> k;
map <int,int> s;
for (int i=min(a,b);i > 0;i--){
    if(a%i==0&&b%i==0){
        s[j]=i;
        //cout << s[j] << endl;
        j++;
    }
}
for (int i = 1;i <= j;i++){
    //cout << s[i] << endl;
    if(i==k){
        cout << s[i] << endl;
        break;
    }
}
}