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: Wrong Answer)

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

namespace ConsoleApp1
{
    class Program
    {
        static void Main(string[] args)
        {
            long H, W, ans = long.MaxValue, sa = 0, sb = 0, sc = 0;
            string[] s = Console.ReadLine().Split(' ');
            H = int.Parse(s[0]);
            W = int.Parse(s[1]);

            if(H % 3 == 0 || W % 3 == 0)
            {
                ans = 0;
            }
            else
            {
                for(int i = 1; i < H; i++)
                {
                    sa = i * W;
                    if(W % 2 == 0)
                    {
                        sb = (H - i) * (W / 2);
                        sc = sb;
                    }
                    else
                    {
                        sb = (H - i) * ((W + 1) / 2);
                        sc = (H - i) * ((W - 1) / 2);
                    }
                    long a = Math.Max(sa, Math.Max(sb, sc)) - Math.Min(sa, Math.Min(sb, sc));
                    ans = Math.Min(ans, a);
                }


                for (uint i = 1; i < W; i++)
                {
                    sa = i * H;
                    if (H % 2 == 0)
                    {
                        sb = (W - i) * (H / 2);
                        sc = sb;
                    }
                    else
                    {
                        sb = (W - i) * ((H + 1) / 2);
                        sc = (W - i) * ((H - 1) / 2);
                    }
                    long a = Math.Max(sa, Math.Max(sb, sc)) - Math.Min(sa, Math.Min(sb, sc));
                    ans = Math.Min(ans, a);
                }
            }

            Console.WriteLine(ans);
        }
    }
}