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.Linq;

namespace ABC062_C
{
    class Program
    {
        static void Main(string[] args)
        {
            var HW = Console.ReadLine().Split().Select(int.Parse).ToArray();
            var H = HW[0];
            var W = HW[1];

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

            var dif = Math.Min(Calc(H, W), Calc(W, H));
            Console.WriteLine(dif);
        }

        public static long Calc(int H, int W)
        {
            var dif = 100000000000;
            for (int i = 1; i < H; i++)
            {
                var t = H - i;
                var rec1 = i * W;
                var rec2 = W % 2 == 0 ? t * W / 2 : t * (W + 1) / 2;
                var rec3 = W % 2 == 0 ? t * W / 2 : t * (W - 1) / 2;

                var casedif = Math.Max(Math.Abs(rec1 - rec2), Math.Max(Math.Abs(rec1 - rec3), Math.Abs(rec2 - rec3)));
                dif = Math.Min(casedif, dif);
            }
            return dif;
        }
    }
}