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.util.Scanner;

public class Main {

	public static void main(String[] args) {
		try (Scanner sc = new Scanner(System.in)) {
			long h = sc.nextLong();
			long w = sc.nextLong();

			if (h % 3 == 0 || w % 3 == 0) {
				System.out.println("0");
				return;
			}

			long ansA = Math.min(calcA(h, w), calcA(w, h));
			long ansB = Math.min(calcB(h, w), calcB(w, h));
			long ansC = Math.min(calcC(h, w), calcC(w, h));
			long ansD = calcB(w, h);
			System.out.println(Math.min(Math.min(ansA, ansB),Math.min(ansC, ansD)));

		}
	}

	private static long calcA(long h, long w) {
		long s1 = 0;
		long s2 = 0;
		long s3 = 0;

		s1 = ((w / 3) + 1) * h;
		long w2 = w - ((w / 3) + 1);
		s2 = w2 * (h / 2);
		long h2 = h - (h / 2);
		s3 = w2 * h2;

		if (s1 == 0 || s2 == 0 || s3 == 0) {
			return Long.MAX_VALUE;
		}

		return Math.max(s1, Math.max(s2, s3)) - Math.min(s1, Math.min(s2, s3));
	}

	private static long calcB(long h, long w) {

		long s1 = 0;
		long s2 = 0;
		long s3 = 0;

		s1 = (w / 3) * h;
		long w2 = w - (w / 3);
		s2 = w2 * (h / 2);
		long h2 = h - (h / 2);
		s3 = w2 * h2;

		if (s1 == 0 || s2 == 0 || s3 == 0) {
			return Long.MAX_VALUE;
		}

		return Math.max(s1, Math.max(s2, s3)) - Math.min(s1, Math.min(s2, s3));
	}

	private static long calcC(long h, long w) {

		long s1 = 0;
		long s2 = 0;
		long s3 = 0;

		s1 = (w / 2) * (h / 2);
		long w2 = w - (w / 2);
		long h2 = h - (h / 2);
		s2 = w * h2;
		s3 = h * w2;
		if (s1 == 0 || s2 == 0 || s3 == 0) {
			return Long.MAX_VALUE;
		}
		return Math.max(s1, Math.max(s2, s3)) - Math.min(s1, Math.min(s2, s3));
	}

}