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 arc074_a
{
    class Program
    {
        static void Main(string[] args)
        {
            long[] x = Console.ReadLine().Split().Select(long.Parse).ToArray();
            Array.Sort(x);
            if (x[0] * x[1] % 3 == 0)
            {
                Console.WriteLine(0);
            }
            else if (x[0] % 2 == 0)
            {
                Console.WriteLine(x[0] / 2);
            }
            else if (x[1] % 2 == 0)
            {
                Console.WriteLine(x[1] / 2);
            }
            else
            {
                Console.WriteLine(Math.Min(x[0], x[1] * (x[0] - 1) / 2 - (x[1] - 1) / 2 * (x[0] + 1) / 2));
            }
        }
    }
}