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<iostream>
using namespace std;
int main() {

	int A = 0;
	int B = 0;
	int K = 0;
	int d = 0;
	int j = 0;
	int s[100] = { 0 };
	cin >> A >> B >> K;
	if (A < B) {
		d = A;
		A = B;
		B = d;
	}
	for (int i = 1; i < B / 2 + 1; i++) {
		if (A % i == 0 && B % i == 0) {
			s[j] = i;
			j++;
		}
	}
	cout << s[K - 1];
}