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.*;

public class Main {
    public static Long getMin(Long x, Long y){
        return (x < y)? x : y;
    }

    public static Long getMax(Long x, Long y){
        return (x > y)? x : y;
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        Long h = sc.nextLong();
        Long w = sc.nextLong();
        Long ans = 0L;

        if(h % 3 != 0 && w % 3 != 0){
            if(h > w){
                Long tmp = h;
                h = w;
                w = tmp;
            }

            Long s = h * w;
            Long smax, smin;
            Long min_h_loop = s;
            for(Long h_loop = 1L; h_loop < h; h_loop++){
                Long s_a = h_loop * w;
                Long s_b = (h - h_loop) * (w / 2);
                Long s_c = s - s_a - s_b;
                smax = getMax(getMax(s_a, s_b), s_c);
                smin = getMin(getMin(s_a, s_b), s_c);
                min_h_loop = getMin(min_h_loop, smax - smin);
            }
            ans = min_h_loop;

            if(h < w){
                Long min_w_loop = s;
                for(Long w_loop = 1L; w_loop < w; w_loop++){
                    Long s_a = w_loop * h;
                    Long s_b = (w - w_loop) * (h / 2);
                    Long s_c = s - s_a - s_b;
                    smax = getMax(getMax(s_a, s_b), s_c);
                    smin = getMin(getMin(s_a, s_b), s_c);
                    min_w_loop = getMin(min_w_loop, smax - smin);
                }
                ans = getMin(ans, min_w_loop);
            }
        }

        System.out.println(ans);
    }    
}