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 Contest
{
    class Program
    {
        static void Main(string[] args)
        {
            ARC074.C();
        }
        class ARC074
        {
            public static void C()
            {
                var H = Read.Long();
                var W = Read.Long();
                Func<long, long, long> func = (A, B) =>
                {
                    long minF = (long)1e18;
                    var from = Math.Max(0, A / 3 - 10);
                    var to = Math.Min(A, A / 3 + 10);
                    for (var i = from; i < to; ++i)
                    {
                        var p1 = i * B;
                        var resA = A - i;
                        var resB = B;
                        var p2a = resA / 2 * resB;
                        var p3a = (resA + 1) / 2 * resB;
                        var p2b = resB / 2 * resA;
                        var p3b = (resB + 1) / 2 * resA;
                        var arrayA = new long[] { p1, p2a, p3a };
                        var arrayB = new long[] { p1, p2b, p3b };
                        minF = Math.Min(minF, arrayA.Max() - arrayA.Min());
                        minF = Math.Min(minF, arrayB.Max() - arrayB.Min());
                    }
                    return minF;
                };
                Console.WriteLine(Math.Min(func(H, W), func(W, H)));
            }
            public static void D()
            {
                var N = Read.Int();
                var A = Read.LongN();

                var X = new long[N + 1];
                {
                    var queue = new Util.PriorityQueue<long>(N + 1);
                    X[0] = A.Take(N).Sum();
                    for(int i = 0; i < N; ++i) { queue.Push(A[i]); }
                    for(int i = 0; i < N; ++i)
                    {
                        var v = A[N + i];
                        queue.Push(v);
                        var w = queue.Pop();
                        X[i + 1] = X[i] - w + v;
                    }
                }
                var Y = new long[N + 1];
                {
                    var queue = new Util.PriorityQueue<long>(N + 1, false);
                    Y[0] = A.Skip(N * 2).Sum();
                    for (int i = 0; i < N; ++i) { queue.Push(A[N * 2 + i]); }
                    for (int i = 0; i < N; ++i)
                    {
                        var v = A[N * 2 - i - 1];
                        queue.Push(v);
                        var w = queue.Pop();
                        Y[i + 1] = Y[i] - w + v;
                    }
                }
                long max = (long)-1e18;
                for(int i = 0; i <= N; ++i)
                {
                    max = Math.Max(max, X[i] - Y[N - i]);
                }
                Console.WriteLine(max);
            }
        }
        class Util
        {
            public class PriorityQueue<T> where T : IComparable
            {
                private IComparer<T> _comparer = null; private bool _isAsc = true; private T[] _heap; private int _sz = 0;
                public PriorityQueue(int maxSize, IComparer<T> comparer) { _heap = new T[maxSize]; _comparer = comparer; }
                public PriorityQueue(int maxSize, bool isAsc = true) { _heap = new T[maxSize]; _isAsc = isAsc; }
                private int Compare(T x, T y) { if (_comparer != null) { return _comparer.Compare(x, y); } return _isAsc ? x.CompareTo(y) : y.CompareTo(x); }
                public void Push(T x) { var i = _sz++; while (i > 0) { var p = (i - 1) / 2; if (Compare(_heap[p], x) <= 0) { break; } _heap[i] = _heap[p]; i = p; } _heap[i] = x; }
                public T Pop() { T ret = _heap[0]; T x = _heap[--_sz]; int i = 0; while (i * 2 + 1 < _sz) { int a = i * 2 + 1; int b = i * 2 + 2; if (b < _sz && Compare(_heap[b], _heap[a]) < 0) { a = b; } if (Compare(_heap[a], x) >= 0) { break; } _heap[i] = _heap[a]; i = a; } _heap[i] = x; return ret; }
                public int Count() { return _sz; }
                public T Peek() { return _heap[0]; }
                public bool Contains(T x) { for (int i = 0; i < _sz; i++) if (x.Equals(_heap[i])) return true; return false; }
            }
        }

        static class Read
        {
            static Queue<string> queue = new Queue<string>();
            static void Enqueue() { var ss = Console.ReadLine().Split(' '); foreach (var s in ss) { queue.Enqueue(s); } }
            public static int Int() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt32(queue.Dequeue()); }
            public static long Long() { if (queue.Count == 0) { Enqueue(); } return Convert.ToInt64(queue.Dequeue()); }
            public static string Str() { if (queue.Count == 0) { Enqueue(); } return queue.Dequeue(); }
            public static int[] IntN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt32(s)).ToArray(); }
            public static long[] LongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToInt64(s)).ToArray(); }
            public static ulong[] ULongN() { return Console.ReadLine().Split(' ').Select(s => Convert.ToUInt64(s)).ToArray(); }
            public static string[] StrN() { return Console.ReadLine().Split(' '); }
            public static Tuple<int, int>[] TupleInt(int n) { List<Tuple<int, int>> list = new List<Tuple<int, int>>(); for (int i = 0; i < n; ++i) { var ab = Read.IntN(); list.Add(new Tuple<int, int>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<long, long>[] TupleLong(int n) { List<Tuple<long, long>> list = new List<Tuple<long, long>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<long, long>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<string, string>[] TupleStr(int n) { List<Tuple<string, string>> list = new List<Tuple<string, string>>(); for (int i = 0; i < n; ++i) { var ab = Read.StrN(); list.Add(new Tuple<string, string>(ab[0], ab[1])); } return list.ToArray(); }
            public static Tuple<double, double>[] TupleDouble(int n) { List<Tuple<double, double>> list = new List<Tuple<double, double>>(); for (int i = 0; i < n; ++i) { var ab = Read.LongN(); list.Add(new Tuple<double, double>(ab[0], ab[1])); } return list.ToArray(); }
            public static long[,] LongMatrix(int r, int c)
            {
                var mat = new long[r, c];
                for (int i = 0; i < r; ++i)
                {
                    var x = Read.LongN();
                    for (int j = 0; j < c; ++j)
                    {
                        mat[i, j] = x[j];
                    }
                }
                return mat;
            }
            public static Dictionary<int, HashSet<int>> AdjacencyList(int N, int M, bool isDirectional = false)
            {
                Dictionary<int, HashSet<int>> dict = new Dictionary<int, HashSet<int>>();
                for (int i = 0; i <= N; ++i) { dict.Add(i, new HashSet<int>()); }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN(); dict[ab[0]].Add(ab[1]);
                    if (!isDirectional) { dict[ab[1]].Add(ab[0]); }
                }
                return dict;
            }
            public static Dictionary<int, Dictionary<int, long>> AdjacencyListWithWeight(int N, int M)
            {
                Dictionary<int, Dictionary<int, long>> dict = new Dictionary<int, Dictionary<int, long>>();
                for (int i = 0; i <= N; ++i)
                {
                    dict.Add(i, new Dictionary<int, long>());
                }
                for (int i = 0; i < M; ++i)
                {
                    var ab = Read.IntN();
                    dict[ab[0]].Add(ab[1], ab[2]);
                    dict[ab[1]].Add(ab[0], ab[2]);
                }
                return dict;
            }
        }
    }
}