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;

namespace ABC062C
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] bufs = Console.ReadLine().Split(' ');
            int H = Int32.Parse(bufs[0]);
            int W = Int32.Parse(bufs[1]);

            long res = 0;

            if (H % 3 != 0 && W % 3 != 0)
            {
                int Af, Bf, Bs, Cf;
                long AS, BS, CS;
                long chk = (long)H * W;
                if (H > W)
                {
                    Af = W;
                    Bf = W / 2 + W % 2;
                    Bs = H - 1;
                    Cf = W / 2;
                }
                else
                {
                    Af = H;
                    Bf = H / 2 + H % 2;
                    Bs = W - 1;
                    Cf = H / 2;
                }
                AS = Af;
                BS = (long)Bf * Bs;
                CS = (long)Cf * Bs;

                long tmpS = Math.Abs(AS - BS);
                int i = 0;

                while(tmpS < chk)
                {
                    i++;
                    chk = tmpS;
                    AS += Af;
                    BS -= Bf;
                    CS -= Cf;
                    tmpS = Math.Abs(AS - BS);
                }

                
                res = Math.Abs((AS - Af) - (CS + Cf));
            }

            Console.WriteLine(res);

        }
    }
}