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.Linq;
using System.Collections.Generic;

namespace Algorithm
{
    class Program
    {
        static void Main(string[] args)
        {
            // 写経
            var HW = Console.ReadLine().Split().Select(long.Parse).ToArray();
            long H = HW[0], W = HW[1];
            var ans = long.MaxValue;

            for (var k = 0; k < 2; k++)
            {
                for (var i = 1; i < H; i++)
                {
                    // T時に分割した時
                    var a = i * W;
                    var b = (W / 2) * (H - i);
                    var c = (W - (W / 2)) * (H - i);
                    ans = Math.Min(ans, Math.Abs(Math.Max(Math.Max(a, b), c) - Math.Min(Math.Min(a, b), c)));

                    // 同じ方向に3分割した時
                    b = W * ((H - i) / 2);
                    c = W * (H - (((H - i) / 2) + i));
                    ans = Math.Min(ans, Math.Abs(Math.Max(Math.Max(a, b), c) - Math.Min(Math.Min(a, b), c)));
                }

                Swap(ref H, ref W);
            }

            Console.WriteLine(ans);
        }

        static void Swap<T>(ref T one, ref T two)
        {
            var temp = one;
            one = two;
            two = temp;
        }
    }
}