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.Generic;
using System.Linq;
using static System.Console;
using static System.Math;
using static System.Array;

class MainClass : Scanner
{
    static void Main()
    {
        var (H, W) = ReadStream<long,long>();
        long ans = long.MaxValue;
        for (int i = 1; i < H; i++)
        {
            var S1 = W * i;
            var Hleft = H - i;
            var (lb, ub) = (1L, W-1);
            while (ub - lb > 1)
            {
                var mid = (lb + ub) / 2;
                if (mid*Hleft<S1) lb = mid;
                else ub = mid;
            }
            var dif1 = Max(S1, Max(Hleft * lb, Hleft * (W - lb))) - Min(S1, Min(Hleft * lb, Hleft * (W - lb)));
            var dif2 = Max(S1, Max(Hleft * ub, Hleft * (W - ub))) - Min(S1, Min(Hleft * ub, Hleft * (W - ub)));
            ans = Math.Min(ans, Min(dif1,dif2));
            
        }
        ans = Min(ans, H * (W / 3 + W % 3) - H * (W / 3));
        for (int i = 1; i < W; i++)
        {
            var S1 = H * i;
            var Wleft = W - i;
            var (lb, ub) = (1L, H-1);
            while (ub - lb > 1)
            {
                var mid = (lb + ub) / 2;
                if (mid * Wleft < S1) lb = mid;
                else ub = mid;
            }
            var dif1 = Max(S1, Max(Wleft * lb, Wleft * (H - lb))) - Min(S1, Min(Wleft * lb, Wleft * (H - lb)));
            var dif2 = Max(S1, Max(Wleft * ub, Wleft * (H - ub))) - Min(S1, Min(Wleft * ub, Wleft * (H - ub)));
            ans = Math.Min(ans, Min(dif1, dif2));
        }
        ans = Min(ans, W * (H / 3 + H % 3) - W * (H / 3));
        WriteLine(ans);
    }
}

class Scanner
{
    public static int RInt() => int.Parse(Console.ReadLine());
    public static long RLong() => long.Parse(Console.ReadLine());
    public static string RString() => Console.ReadLine();
    public static double RDouble() => double.Parse(Console.ReadLine());

    public static int[] RInts() => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    public static int[] RInts(Func<string, int> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static long[] RLongs() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    public static long[] RLongs(Func<string, long> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static double[] RDoubles() => Array.ConvertAll(Console.ReadLine().Split(), double.Parse);
    public static double[] RDoubles(Func<string, double> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static string[] RStrings() => Console.ReadLine().Split();
    //public static string[] RStrings(Func<string, string> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static T1 ReadStream<T1>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        return r1;
    }
    public static (T1, T2) ReadStream<T1, T2>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        return (r1, r2);
    }
    public static (T1, T2, T3) ReadStream<T1, T2, T3>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        return (r1, r2, r3);
    }
    public static (T1, T2, T3, T4) ReadStream<T1, T2, T3, T4>()
    {
        var r = RStrings();
        var r1 = (T1)Convert.ChangeType(r[0], typeof(T1));
        var r2 = (T2)Convert.ChangeType(r[1], typeof(T2));
        var r3 = (T3)Convert.ChangeType(r[2], typeof(T3));
        var r4 = (T4)Convert.ChangeType(r[3], typeof(T4));
        return (r1, r2, r3, r4);
    }
}