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 9.2.1) (judge verdict: Accepted)

#include <bits/stdc++.h>
#define rep0(i, n) for (int i = 0; i < (n); ++i)
#define rep1(i, n) for (int i = 1; i <= (n); ++i)
using namespace std;
typedef long long ll;
typedef pair<int, int> P;
typedef tuple<string, int, int> TU;
typedef tuple<int, int, int> TI;

int main()
{
    int a,b,k;
    cin >> a >> b >> k;
    ll res=0;
    ll now=__gcd(a,b);
    while(k>0){
        if(a%now==0&&b%now==0){
            k--;
        }
        now--;
    }
    cout << now+1 << endl;
}