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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Collections;
using System.Linq.Expressions;

static class Program
{
    static void Main()
    {
        new Magatro().Solve();
    }
}

class Magatro
{
    private long H, W;
    private void Scan()
    {
        var line = Console.ReadLine().Split(' ');
        H = long.Parse(line[0]);
        W = long.Parse(line[1]);
    }

    public void Solve()
    {
        Scan();

        long ans = long.MaxValue;
        for (int i = 0; i <= H; i++)
        {
            long a = W * i;
            long b = ((W + 1) / 2) * (H - i);
            long c = (W / 2) * (H - i);
            long max = Math.Max(Math.Max(a, b), c);
            long min = Math.Min(Math.Min(a, b), c);
            ans = Math.Min(ans, max - min);
            b = W * ((H - i) / 2);
            c = W * ((H - i + 1) / 2);
            max = Math.Max(Math.Max(a, b), c);
            min = Math.Min(Math.Min(a, b), c);
            ans = Math.Min(ans, max - min);
        }
        for (int i = 0; i <= W; i++)
        {
            long a = H * i;
            long b = ((H + 1) / 2) * (W - i);
            long c = (H / 2) * (W - i);
            long max = Math.Max(Math.Max(a, b), c);
            long min = Math.Min(Math.Min(a, b), c);
            ans = Math.Min(ans, max - min);
            b = H * ((W - i) / 2);
            c = H * ((W - i + 1) / 2);
             max = Math.Max(Math.Max(a, b), c);
             min = Math.Min(Math.Min(a, b), c);
            ans = Math.Min(ans, max - min);
        }
        Console.WriteLine(ans);
    }
}