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: Runtime Error)

//#pragma warning disable

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

public class Test
{
    public static void Main()
    {
        var N = long.Parse(Console.ReadLine());

        var a = Console.ReadLine().Split(' ').Select(long.Parse).ToArray();

        // Xの値の配列を作成
        long[] X = new long[N + 1];
        {
            var list = new SortedSet<long>();  // 降順
            for (int i = 0; i < N - 1; i++)
            {
                list.Add(-a[i]);
            }

            for (int i = (int)N - 1; i < 2 * N; i++)
            {
                list.Add(-a[i]);

                // list の最初の(大きい方の) N 個の総和
                X[i - N + 1] = -list.Take((int)N).Sum();
            }
        }

        // Yの値の配列を作成
        long[] Y = new long[N + 1];
        {
            var list = new SortedSet<long>();  // 昇順
            for (int i = 3 * (int)N - 1; i >= 2 * N + 1; i--)
            {
                list.Add(a[i]);
            }

            for (int i = 2 * (int)N; i >= N; i--)
            {
                list.Add(a[i]);

                // list の最初の(小さい方の) N 個の総和
                Y[i - N] = list.Take((int)N).Sum();
            }
        }

        //Console.WriteLine(String.Join(", ", X));
        //Console.WriteLine(String.Join(", ", Y));

        var result = X.Zip(Y, (x, y) => (x - y)).Max();

        Console.WriteLine(result);
    }
}