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.InputStreamReader;


public class Main {
    public static void main(String[] args) {
        Main main = new Main();
        main.solve(args);
    }

    public void solve(String[] args) {
        MyScanner scanner = new MyScanner();

        // 数取得
        int a = scanner.nextInt();
        int b = scanner.nextInt();
        int k = scanner.nextInt();


        // ループの開始
        int n = 0;
        if(a>b){
        	n=b;
        }else {
        	n=a;
        }

        // カウンタ
        int cnt = 0;

        for(int i=n;i>0;i--) {
        	if((a%i==0)&&(b%i==0)) {
        		cnt++;
        		if(cnt==k) {
        			System.out.println(i);
        			break;
        		}
        	}
        }
    }

    private class MyScanner {
        String[] s;
        int i;
        BufferedReader br;
        String reg = " ";
        MyScanner () {
            s = new String[0];
            i = 0;
            br = new BufferedReader(new InputStreamReader(System.in));
        }
        public String next() {
            try {
                if (i < s.length) return s[i++];
                String line = br.readLine();
                while (line.equals("")) {line = br.readLine();}
                s = line.split(reg, 0);
                i = 0;return s[i++];
            } catch (Exception e) {e.printStackTrace();}
            return null;
        }
        public int nextInt() {
            try {return Integer.parseInt(next());} catch (Exception e) {e.printStackTrace();}
            return -1;
        }
        public double nextDouble() {
            try {return Double.parseDouble(next());} catch (Exception e) {e.printStackTrace();}
            return -1;
        }
        public long nextLong()  {
            try {return Long.parseLong(next());} catch (Exception e) {e.printStackTrace();}
            return -1;
        }
    }
}