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)

#pragma warning disable
using System.Collections.Generic;
using System.IO;
using System.Linq;
using System;
using System.Collections;
using static System.Math;
using static System.Console;

class E { static void Main() => new J(); }
class J
{
	const int Mod = 1000000007;
	int F() => int.Parse(ReadLine());
	int[] G() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(int.Parse).ToArray();
	public J()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		Solve();
		Out.Flush();
	}
	void Solve()
	{
		var I = G();
		WriteLine(Min(Z(I[0], I[1]), Z(I[1], I[0])));
	}
	long Z(long X, long Y)
	{
		var ans = X * Y;
		for (var x = 1; x < X; x++)
		{
			var f = F(X - x, Y);
			var k = x * Y;
			ans = Min(ans, Max(f.Item2, k) - Min(f.Item1, k));
		}
		return ans;
	}
	Tuple<long, long> F(long X, long Y)
	{
		var mx = X / 2;
		var my = Y / 2;
		var a = new Tuple<long, long>(mx * Y, (X - mx) * Y);
		var b = new Tuple<long, long>(X * my, (Y - my) * X);
		var da = a.Item2 - a.Item1;
		var db = b.Item2 - b.Item1;
		if (da <= db) return a;
		else return b;
	}
	long GCD(long a, long b)
	{
		var n = (ulong)Abs(a); var m = (ulong)Abs(b);
		if (n == 0) return (long)m; if (m == 0) return (long)n;
		int zm = 0, zn = 0;
		while ((n & 1) == 0) { n >>= 1; zn++; }
		while ((m & 1) == 0) { m >>= 1; zm++; }
		while (m != n)
		{
			if (m > n) { m -= n; while ((m & 1) == 0) m >>= 1; }
			else { n -= m; while ((n & 1) == 0) n >>= 1; }
		}
		return (long)n << Min(zm, zn);
	}
}