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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using static System.Console;
using static System.Math;
using static MyExtention;
class MainClass : Scanner
{
    static void Main()
    {
        var (H, W) = ReadTuple<long,long>();
        long a, b, c;
        long ans = long.MaxValue;
        for (int i = 0; i <= H; i++)
        {
            long leftH = H - i;
            a = W * i;
            b = W / 2 * leftH;
            c = (W - W / 2) * leftH;
            long min = Min(a, b, c);
            long max = Max(a, b, c);
            ans = Min(ans, max - min);
        }

        {
            a = H / 3 * W;
            long leftH = H - H / 3;
            b = leftH / 2 * W;
            c = (leftH - leftH / 2) * W;

            long min = Min(a, b, c);
            long max = Max(a, b, c);
            ans = Min(ans, max - min);
        }

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

        {
            a = W / 3 * H;
            long leftW = W - W / 3;
            b = leftW / 2 * H;
            c = (leftW - leftW / 2) * H;
            long min = Min(a, b, c);
            long max = Max(a, b, c);
            ans = Min(ans, max - min);
        }

        WriteLine(ans);
    }
}

class MyExtention
{
    public static long GCD(long a, long b)
        => a == 0 ? b : GCD(b % a, a);
    public static long LCM(long a, long b)
        => a / GCD(a, b) * b;

    public static long ModPow(long a, long n, long Mod) //未テスト　オーバーフローの可能性あり
    {
        long ans = 1;
        while (n > 0)
        {
            if (n % 2 == 1)
                ans = ans * a % Mod;
            a = a * a % Mod;
            n /= 2;
        }
        return ans;
    }
    public static T Max<T>(params T[] nums) where T : IComparable
    {
        T max = nums[0];
        for (int i = 1; i < nums.Length; i++)
        {
            if (max.CompareTo(nums[i]) < 0) max = nums[i];
        }
        return max;
    }
    public static T Min<T>(params T[] nums) where T : IComparable
    {
        T min = nums[0];
        for (int i = 1; i < nums.Length; i++)
        {
            if (min.CompareTo(nums[i]) > 0) min = nums[i];
        }
        return min;
    }


}

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

    public static string[] RStrings() => Console.ReadLine().Split();
    public static int[] RInts() => Array.ConvertAll(Console.ReadLine().Split(), int.Parse);
    public static long[] RLongs() => Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
    public static double[] RDoubles() => Array.ConvertAll(Console.ReadLine().Split(), double.Parse);
    public static int[] RInts(Func<string, int> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static long[] RLongs(Func<string, long> func) => Console.ReadLine().Split().Select(func).ToArray();
    public static double[] RDoubles(Func<string, double> func) => Console.ReadLine().Split().Select(func).ToArray();
    //public static string[] RStrings(Func<string, string> func) => Console.ReadLine().Split().Select(func).ToArray();

    public static T1 ReadTuple<T1>()
    {
        var r = RString();
        var r1 = (T1)Convert.ChangeType(r, typeof(T1));
        return r1;
    }
    public static (T1, T2) ReadTuple<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) ReadTuple<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) ReadTuple<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);
    }
}