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 <stdlib.h>
#include <stdio.h>
#include <time.h>
#include <math.h>
#include <iostream>
#include <string>
#include<algorithm>
#include <vector>
#include <cassert>
#include<cmath>
using namespace std;
int main() {
	int A, B, K;
	int  A_div, B_div = 0;
	int i, j;
	int ans[100] = {};
	int res = 0;
	cin >> A >> B >> K;
	
	for (i = 1; i < 100; ++i) {
		A_div = A % i;
		B_div = B % i;
		if (A_div==0&&B_div==0) {
			ans[res] = i;
			++res;
			//cout << i << endl;
		}

	}

	cout << ans[res - K] << endl;




}