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();
		long ans = 100000 * 100000, max = 0, min = 0, a = 0, b = 0, c = 0;
		int j = 0;

		if ((h * w) % 3 != 0) {
			// 縦割
			j = w / 3;
			max = 0;
			min = 0;
			a = h * j;
			b = h * (w - j) / 2;
			c = h * (w - ((w - j) / 2));
			System.out.println("1a:"+a+" b:"+b+" c:"+c);
			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;
				System.out.println("1max:"+max+" min:"+min+" ans:"+ans);
			}

			// 横割
			j = h / 3;
			max = 0;
			min = 0;
			a = w * j;
			b = w * (h - j) / 2;
			c = w * (h - ((h - j) / 2));
			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;
				System.out.println("2max:"+max+" min:"+min+" ans:"+ans);
			}

			// 縦T
			for (int i = 1; i < h; i++) {
				j = w / 2;
				max = 0;
				min = 0;
				a = i * w;
				b = (h - i) * j;
				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;
					System.out.println("3max:"+max+" min:"+min+" ans:"+ans);
				}
			}

			// 横T
			for (int i = 1; i < w; i++) {
				j = h / 2;
				max = 0;
				min = 0;
				a = h * i;
				b = j * (w - i);
				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;
					System.out.println("4max:"+max+" min:"+min+" ans:"+ans);
				}
			}
		} else {
			ans = 0;
		}

		System.out.println(ans);

		sc.close();
	}
}