Problem:
Score : 400 points

Problem Statement

There is a bar of chocolate with a height of H blocks and a width of W blocks.
Snuke is dividing this bar into exactly three pieces.
He can only cut the bar along borders of blocks, and the shape of each piece must be a rectangle.

Snuke is trying to divide the bar as evenly as possible.
More specifically, he is trying to minimize S_{max} - S_{min}, where S_{max} is the area (the number of blocks contained) of the largest piece, and S_{min} is the area of the smallest piece.
Find the minimum possible value of S_{max} - S_{min}.

Constraints

2 ≤ H, W ≤ 10^5

Input

Input is given from Standard Input in the following format:

H W

Output

Print the minimum possible value of S_{max} - S_{min}.

Sample Input 1

3 5

Sample Output 1

0

In the division below, S_{max} - S_{min} = 5 - 5 = 0.

Sample Input 2

4 5

Sample Output 2

2

In the division below, S_{max} - S_{min} = 8 - 6 = 2.

Sample Input 3

5 5

Sample Output 3

4

In the division below, S_{max} - S_{min} = 10 - 6 = 4.

Sample Input 4

100000 2

Sample Output 4

1

Sample Input 5

100000 100000

Sample Output 5

50000

Solution in Java (OpenJDK 11.0.6) (judge verdict: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.Scanner;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        Scanner in = new Scanner(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        ChocolateBar solver = new ChocolateBar();
        solver.solve(1, in, out);
        out.close();
    }

    static class ChocolateBar {
        public void solve(int testNumber, Scanner in, PrintWriter out) {
            long h = in.nextLong();
            long w = in.nextLong();

            long result = Long.MAX_VALUE;
            // 横割り
            for (long i = 0; i <= h; i++) {
                // 横割り
                long hh = h - i;
                long h2 = hh / 2;
                long h3 = hh - h2;
                long res = Math.max(Math.max(i * w, h2 * w), h3 * w) - Math.min(Math.min(i * w, h2 * w), h3 * w);
                result = Math.min(result, res);

                // 縦割り
                long w2 = w / 2;
                long w3 = w - w2;
                long res2 = Math.max(Math.max(i * w, hh * w2), hh * w3) - Math.min(Math.min(i * w, hh * w2), hh * w3);
                result = Math.min(result, res2);
            }
            // 縦割り
            for (long i = 0; i <= w; i++) {
                // 横割り
                long ww = w - i;
                long h2 = h / 2;
                long h3 = h - h2;
                long res = Math.max(Math.max(i * h, h2 * ww), h3 * ww) - Math.min(Math.min(i * h, h2 * ww), h3 * ww);
                result = Math.min(result, res);

                // 縦割り
                long w2 = ww / 2;
                long w3 = ww - w2;
                long res2 = Math.max(Math.max(i * h, h * w2), h * w3) - Math.min(Math.min(i * h, h * w2), h * w3);
                result = Math.min(result, res2);
            }
            out.println(result);
        }

    }
}