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.Linq;
using System;

public class Hello
{
    public static void Main()
    {
        string[] line = Console.ReadLine().Trim().Split(' ');
        var h = long.Parse(line[0]);
        var w = long.Parse(line[1]);
        if (h % 3 == 0 | w % 3 == 0) { Console.WriteLine(0); goto end; }
        var r1 = Math.Min(getDD3(h, w), getDD3(w, h));
        var r2 = Math.Min(getD3(h, w), getD3(w, h));
        var r3 = Math.Min(r1, r2);
        Console.WriteLine(r3);
        end:;
    }
    public static long getDD3(long a, long b)
    {
        var b1 = b / 2;
        var b2 = b - b1;
        var ret = 9999999999999999L;
        for (int i = 1; i < a; i++)
        {
            var x = getABSmin(b1 * (a - i), b2 * (a - i), b * i);
            ret = Math.Min(ret, x);
        }
        return ret;
    }
    public static long getABSmin(long a, long b, long c)
    {
        var ar = new long[3];
        ar[0] = a; ar[1] = b; ar[2] = c;
        return ar.Max() - ar.Min();
    }
    public static long getD3(long a, long b)
    {
        var ret = 9999999999999L;
        for (int i = 1; i <= b - 2; i++)
        {
            var w1 = (b - i) / 2;
            var w2 = b -  i -  w1;
            ret = Math.Min(ret, getABSmin(w1, w2, i));
        }
        return ret * a;
    }
}