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 abc62
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] str = Console.ReadLine().Split(' ');
            int H = int.Parse(str[0]);
            int W = int.Parse(str[1]);
            int ans = 0;
            if (H % 3 == 0 || W % 3 == 0)
            {
                ans = 0;
            }else
            {
                int ans1 = 0;
                int ans2 = 0;
                if (H % 2 == 0)
                {
                    ans1 = H / 2;
                }else
                {
                    int a = W / 3;
                    int b = H / 2;
                    if (W % 3 == 1)
                    {
                        ans1 = Math.Min(Math.Max(a + 2 * b + 1, 2 * a), Math.Max(2 * a + 1, a + b + 1));
                    }else
                    {
                        ans1 = Math.Max(2 * a + 1, a + b + 1);
                    }
                }
                if (W % 2 == 0)
                {
                    ans2 = W / 2;
                }
                else
                {
                    int a = H / 3;
                    int b = W / 2;
                    if (H % 3 == 1)
                    {
                        ans2 = Math.Min(Math.Max(a + 2 * b + 1, 2 * a), Math.Max(2 * a + 1, a + b + 1));
                    }
                    else
                    {
                        ans2 = Math.Max(2 * a + 1, a + b + 1);
                    }
                }
                ans = Math.Min(ans1, ans2);


            }
            Console.WriteLine(ans);
        }
    }
}