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<iostream>
#include<string>
#include<vector>
#include<math.h>
#include<algorithm>
#include<cstdio>
#include<stdio.h>
#include<stack>
#include<sstream>
typedef long long ll;

#define pi 3.14159265358979323846
#define VI vector<int>
#define VLL vector<long long>
#define MAX max_element
#define MIN min_element
#define all(v) v.begin(), v.end()

using namespace std;

template<typename T>
T gcd(T a, T b) {
	return b ? gcd(b, a % b) : a;
}
template<typename T>
T lcm(T a, T b) {
	return a * b / gcd(a, b);
}

template<typename T>
T finder(vector<T> vec, T number) {
	auto itr = find(vec.begin(), vec.end(), number);
	size_t index = distance(vec.begin(), itr);
	if (index != vec.size()) { // 発見できたとき
		return 1;
	}
	else { // 発見できなかったとき
		return 0;
	}
}

/*char r[4];
int yaju[4];
char op[3];
int sum = 0;
scanf("%s", r);
for (int i = 0;i < 4;i++) {
	yaju[i] = r[i] - '0';
}
*/

int main() {
	long long A,B,K,ans=1; cin >> A>>B>>K;
	for (int i = A;;i--) {
		if (A % i == 0 && B % i == 0) {
			if (ans == K) {
				cout << i << endl;
				break;
			}
			ans++;
		}
	}
}