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# (.NET Core 3.1.201) (judge verdict: Wrong Answer)

using System;
using System.Collections;
using System.Collections.Generic;
using System.IO;
using System.Linq;

namespace C
{
    public class Program
    {
        static void Main(string[] args)
        {
            var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            Console.SetOut(sw);
            Solve();
            Console.Out.Flush();
        }

        public static void Solve()
        {
            var HW = Console.ReadLine().Trim().Split(' ').Select(long.Parse).ToArray();
            var (H, W) = (HW[0], HW[1]);
            var answer = 0L;
            if (H % 3 != 0 && W % 3 != 0)
            {
                answer = (long)1e10 + 1;
                for (var h = 1; h < H; h++)
                {
                    var S = new long[3];
                    S[0] = h * W;
                    S[1] = (H - h) * ((W + 1) / 2);
                    S[2] = (H - h) * (W / 2);
                    var diff = S.Max() - S.Min();
                    answer = Math.Min(answer, diff);
                }
                for (var w = 1; w < W; w++)
                {
                    var S = new long[3];
                    S[0] = w * H;
                    S[1] = (W - w) * ((H + 1) / 2);
                    S[2] = (W - w) * (H / 2);
                    var diff = S.Max() - S.Min();
                    answer = Math.Min(answer, diff);
                }
            }

            Console.WriteLine(answer);
        }
    }
}