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) {
		Scanner sc = new Scanner((System.in));
		int h = sc.nextInt();
		int w = sc.nextInt();
		int ans = 200000, max = 0, min = 0;
		boolean cal = false;

		if ((h * w) % 3 != 0) {
			// 縦T
			for (int i = 1; i < h; i++) {
				for (int j = 1; j < w; j++) {
					max = 0;
					min = 0;
					int a = i * w;
					int b = (h - i) * j;
					int c = (h - i) * (w - j);
					if (a >= b && a >= c) {
						max = a;
					} else if (b >= a && b >= c) {
						max = b;
					} else {
						max = c;
					}
					if (a <= b && a <= c) {
						min = a;
					} else if (b <= a && b <= c) {
						min = b;
					} else {
						min = c;
					}
					if (ans > (max - min)) {
						ans = max - min;
						cal = true;
					} else if (cal) {
						cal = false;
						break;
					}
				}
			}

			// 横T
			for (int i = 1; i < w; i++) {
				for (int j = 1; j < h; j++) {
					max = 0;
					min = 0;
					int a = h * i;
					int b = j * (w - i);
					int c = (h - j) * (w - i);
					if (a >= b && a >= c) {
						max = a;
					} else if (b >= a && b >= c) {
						max = b;
					} else {
						max = c;
					}
					if (a <= b && a <= c) {
						min = a;
					} else if (b <= a && b <= c) {
						min = b;
					} else {
						min = c;
					}
					if (ans > (max - min)) {
						ans = max - min;
						cal = true;
					} else if (cal) {
						cal = false;
						break;
					}
				}
			}
		} else {
			ans = 0;
		}

		System.out.println(ans);

		sc.close();
	}
}