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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.io.FileNotFoundException;
import java.util.Arrays;
import java.util.Scanner;
import java.util.concurrent.SynchronousQueue;

public class Main {
	public static void main(String[] args) throws FileNotFoundException {
		new Main().run();
	}

	void run() throws FileNotFoundException {
		Scanner sc = new Scanner(System.in);
		long H = sc.nextLong();
		long W = sc.nextLong();
		long ans = Long.MAX_VALUE / 16;
		ans = Math.min(ans, solve(H, W));
		ans = Math.min(ans, solve(W, H));
		System.out.println(ans);
	}

	long solve(long H, long W) {
		long ans = Long.MAX_VALUE / 16;
		if (W / 3 != 0 && W - W / 3 * 2 != 0)
			ans = H * (Math.max(W / 3, W - W / 3 * 2) - Math.min(W / 3, W - W / 3 * 2));
		for (long i = 1; i < H; ++i) {
			ans = Math.min(ans, max(i * W, (H - i) * (W / 2), (H - i) * (W - W / 2))
					- min(i * W, (H - i) * (W / 2), (H - i) * (W - W / 2)));
			long w = i * W / (H - i);
			for (long j = w - 1; j <= w + 1; ++j) {
				if (j <= 0 || W - j <= 0)
					continue;
				ans = Math.min(ans,
						max(i * W, (H - i) * w, (H - i) * (W - w)) - min(i * W, (H - i) * w, (H - i) * (W - w)));
			}
		}
		return ans;
	}

	long max(long a, long b, long c) {
		long ret = a;
		ret = Math.max(ret, b);
		ret = Math.max(ret, c);
		return ret;
	}

	long min(long a, long b, long c) {
		return -max(-a, -b, -c);
	}

	private static void tr(Object... o) {
		System.out.println(Arrays.deepToString(o));
	}
}