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 Java7 (OpenJDK 1.7.0) (judge verdict: Wrong Answer)

import java.io.*;

public class Main {

    public static void main(String[] args) throws IOException {

        BufferedReader reader = new BufferedReader(new InputStreamReader(System.in));

        String[] values = reader.readLine().split(" ");
        int h = Integer.valueOf(values[0]);
        int w = Integer.valueOf(values[1]);


        if (h % 3 == 0 || w % 3 == 0) {
            System.out.print(0);
            return;
        }

        long WH = w*h;

        if (h % 2 == 0 || w % 2 != 0) {
            long area1 = (w / 2 + 1) * h * 3 / 2;
            long area2 = (w / 2 - 1) * h * 3 / 2;
            long min = Math.abs(area1 - WH);
            if (Math.abs(area2 - WH) < min) {
                min = Math.abs(area2 - WH);
            }
            System.out.print(min);
            return;
        } else if (h % 2 != 0 || w % 2 == 0) {
            long area1 = (h / 2 + 1) * w * 3 / 2;
            long area2 = (h / 2 - 1) * w * 3 / 2;
            long min = Math.abs(area1 - WH);
            if (Math.abs(area2 - WH) < min) {
                min = Math.abs(area2 - WH);
            }
            System.out.print(min);
            return;
        }


//        PrintWriter writer = new PrintWriter(new OutputStreamWriter(System.out));
//        writer.close();

    }
}