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.util.*;

public class Main {

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        int H = sc.nextInt();
        int W = sc.nextInt();
        System.out.println( solve(H, W) );
    }

    private static int solve(int H, int W) {
        int tate3 = calcTate3(H, W);
        int yoko3 = calcTate3(W, H);
        int tateYoko = calcTateYoko(H, W);
        int yokoTate = calcTateYoko(W, H);

        return Math.min(Math.min(tate3, yoko3), Math.min(tateYoko, yokoTate));
    }

    private static int calcTate3(int H, int W) {
        if( W < 3 ) return Integer.MAX_VALUE;

        if( W % 3 == 0 ) {
            return 0;
        } else {
            return H;
        }
    }

    // 縦に切った後、横に切る
    private static int calcTateYoko(int H, int W) {
        // 余りを割り振る
        int hq = H / 3;
        int hr = H % 3;

        int h1;
        if( hr == 0 ) {
            h1 = hq;
        } else if( hr == 1 ) {
            h1 = hq;
        } else {
            h1 = hq + 1;
        }
        int h2 = H - h1;

        int wq = W / 2;
        int wr = W % 2;

        int w1 = wr == 1 ? wq + 1 : wq;
        int w2 = W - w1;

        int c1 = h1 * W;
        int c2 = h2 * w1;
        int c3 = h2 * w2;

        int max = Math.max(Math.max(c1, c2), c3);
        int min = Math.min(Math.min(c1, c2), c3);
        return max - min;
    }
}