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 Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;

class Main {
	public static void main(String args[]) throws IOException {
		BufferedReader in = new BufferedReader(new InputStreamReader(System.in));
		Solver solver = new Solver();
		solver.init();
		solver.readHead(in.readLine());
		// for (; solver.hasNext();) {
		// solver.readBody(in.readLine());
		// }
		// solver.solve();
	}
}

class Solver {
	int N;
	int cnt;

	public void init() {
		N = 0;
		cnt = 0;
	}

	public void readHead(String str) {
		String[] strArr = str.split(" ");
		N = Integer.parseInt(strArr[0]);
		// System.out.println(N);
		int a = Integer.parseInt(strArr[0]);
		int b = Integer.parseInt(strArr[1]);
		int k = Integer.parseInt(strArr[2]);
		for (int ans = Integer.min(a, b);; ans--) {
			if (a % ans == 0 && b % ans == 0)
				k--;
			if (k <= 0) {
				System.out.println(ans);
				return;
			}
		}
	}

	public boolean hasNext() {
		return cnt < N;
	}

	public void readBody(String str) {
		// System.out.println(str);
		cnt++;
	}

	public void solve() {

	}
}