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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace ABC062C
{
    class Program
    {
        static int H, W;

        static long calc(int t1, int p1, int t2, int p2)
        {
            int[] s = new int[3];
            int h = H;
            int w = W;
            
            if(t1 == 0)
            {
                if (p1 == 0)
                {
                    if (h / 3 == 0)
                        return long.MaxValue;
                    s[0] = h / 3 * w;
                    h = h - h / 3;
                    if (h == 0)
                        return long.MaxValue;
                }
                else
                {
                    s[0] = (h / 3 + 1) * w;
                    h = h - (h / 3 + 1);
                    if (h == 0)
                        return long.MaxValue;
                }
            }
            else
            {
                if (p1 == 0)
                {
                    if (w / 3 == 0)
                        return long.MaxValue;
                    s[0] = h * w / 3;
                    w = w - w / 3;
                    if (w == 0)
                        return long.MaxValue;
                }
                else
                {
                    s[0] = h * (w / 3 + 1);
                    w = w - (w / 3 + 1);
                    if (w == 0)
                        return long.MaxValue;
                }

            }

            if(t2 == 0)
            {
                if(p2 == 0)
                {
                    if (h / 2 == 0)
                        return long.MaxValue;
                    s[1] = h / 2 * w;
                    h = h - h / 2;
                    s[2] = h * w;
                }
                else
                {
                    s[1] = (h / 2 + 1) * w;
                    h = h - (h / 2 + 1);
                    s[2] = h * w;
                }
            }
            else
            {
                if(p2 == 0)
                {
                    if (w / 2 == 0)
                        return long.MaxValue;
                    s[1] = h * w / 2;
                    w = w - w / 2;
                    s[2] = h * w;
                }
                else
                {
                    s[1] = h * (w / 2 + 1);
                    w = w - (w / 2 + 1);
                    s[2] = h * w;
                }
            }

            Array.Sort(s);
            return Math.Abs(s[2] - s[0]);

        }


        static void Main(string[] args)
        {
            string[] vals = Console.ReadLine().Split(' ');
            H = int.Parse(vals[0]);
            W = int.Parse(vals[1]);

            long[] ans = new long[16];

            ans[0] = calc(0, 0, 0, 0);
            ans[1] = calc(0, 0, 0, 1);
            ans[2] = calc(0, 0, 1, 0);
            ans[3] = calc(0, 0, 1, 1);
            ans[4] = calc(0, 1, 0, 0);
            ans[5] = calc(0, 1, 0, 1);
            ans[6] = calc(0, 1, 1, 0);
            ans[7] = calc(0, 1, 1, 1);
            ans[8] = calc(1, 0, 0, 0);
            ans[9] = calc(1, 0, 0, 1);
            ans[10] = calc(1, 0, 1, 0);
            ans[11] = calc(1, 0, 1, 1);
            ans[12] = calc(1, 1, 0, 0);
            ans[13] = calc(1, 1, 0, 1);
            ans[14] = calc(1, 1, 1, 0);
            ans[15] = calc(1, 1, 1, 1);

            Array.Sort(ans);
            Console.WriteLine(ans[0]);

        }
    }
}