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 Chocolate_Bar
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] line = Console.ReadLine().Split(' ');
            int H = Int32.Parse(line[0]);
            int W = Int32.Parse(line[1]);

            W = Math.Max(Int32.Parse(line[0]),Int32.Parse(line[1]));
            H = Math.Min(Int32.Parse(line[0]), Int32.Parse(line[1]));

            if (W % 3 == 0 || H % 3 == 0)
            {
                Console.WriteLine(0);

            }

            if(H == 2)
            {
                if(W % 3 == 0)
                {
                    Console.WriteLine(0);
                }

               if(W % 3 == 1)
                {
                    Console.WriteLine(1);
                }

               if(W % 3 == 2)
                {
                    Console.WriteLine(2);
                }


            }

            else
            {

                if (W % 2 != 0 && H % 2 == 0)
                {
                    Console.WriteLine(W / 2 * H - H / 2 * (W / 2 + 1));
                }

                if (W % 2 != 0 && H % 2 != 0)
                {
                    Console.WriteLine(W / 2 * H - (H / 2) * (W / 2 + 1));
                }

                if (W % 2 == 0 && H % 2 == 0)
                {
                    Console.WriteLine(W / 2 * H - W / 2 * H / 2);
                }

                if (W % 2 == 0 && H % 2 != 0)
                {
                    Console.WriteLine(W / 2 * H - W / 2 * (H / 2 + 1));
                }
            }
           
            Console.ReadLine();
        }
    }
}