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 Java8 (OpenJDK 1.8.0) (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
 *
 * @author mikit
 */
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);
        CChocolateBar solver = new CChocolateBar();
        solver.solve(1, in, out);
        out.close();
    }

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

            if (h * w % 3 == 0) {
                out.println(0);
                return;
            }

            long ans = Math.min(h, w);
            for (int x = 0; x <= w; x++) {
                long s1 = (w - x) * h;
                long s2 = x * (h / 2);
                long s3 = x * ((h + 1) / 2);
                ans = Math.min(ans, Math.max(s1, s3) - Math.min(s1, s2));
            }
            for (int y = 0; y <= h; y++) {
                long s1 = w * (h - y);
                long s2 = (w / 2) * y;
                long s3 = ((w + 1) / 2) * y;
                ans = Math.min(ans, Math.max(s1, s3) - Math.min(s1, s2));
            }
            out.println(ans);
        }

    }
}