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;

typedef long long ll;

#define REP(i, n) for(int i=0; i<(n); i++)
#define REPS(i, n) for(int i=0; i<=(n); i++)
#define FOR(i, a, b) for(int i=a; i<(b); i++)
#define FORS(i, a, b) for(int i=a; i<=(b); i++)
// for container x
#define ALL(v) (v).begin(),(v).end()
#define RALL(v) (v).rbegin(),(v).rend()
#define SIZE(v) ((ll)(v).size())
#define MAX(v) *max_element(ALL(v))
#define MIN(v) *min_element(ALL(v))
#define UNIQUE(v) v.erase(unique(ALL(v)), v.end())

struct cww{cww(){ios::sync_with_stdio(false);cin.tie(0);}}star;

int main(){
    int A, B, K;
    cin >> A >> B >> K;
    vector<int> divide_des;

    for (int i=min(A, B); i>0; i--){
        if (A%i==0 && B%i==0) divide_des.push_back(i);
    }
    cout << divide_des.at(K-1) << endl;
    return 0;
}