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: Wrong Answer)

import java.util.Scanner;
public class Main {
    public static void main(String[] args) {
        Scanner scan = new Scanner(System.in);
        int H = scan.nextInt();
        int W = scan.nextInt();
        if (H%3 == 0 || W%3 == 0) {
            System.out.println(0);
            return;
        }
        long ans = Integer.MAX_VALUE;
        int w1 = W/2;
        int w2 = W-w1;
        int h1 = H/2;
        int h2 = H-h1;
        for(int i = 1; i <= H/2; i++) {
            long h = W*i;
            long amari1 = (H-i)*w1;
            long amari2 = (H-i)*w2;
            long maxa = Math.max(amari1, amari2);
            long mina = Math.min(amari1, amari2); 
            long max = Math.max(h, maxa);
            long min = Math.min(h, mina);
            if (max-min < ans) {
                ans = max-min;
            }
            //System.out.println("h: "+h+" "+maxa+" "+mina+" "+ans);
        }
        for (int i = 1; i <= W/2; i++) {
            long w = H*i;
            long amari1 = (W-i)*h1;
            long amari2 = (W-i)*h2;
            long maxa = Math.max(amari1, amari2);
            long mina = Math.min(amari1, amari2);
            long max = Math.max(w, maxa);
            long min = Math.min(w, mina);
            if (max - min < ans) {
                ans = max - min;
            }
            //System.out.println("w: "+w+" "+maxa+" "+mina+" "+ans);
        }
        System.out.println(ans);
    }
}