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.Arrays;
import java.util.Scanner;

public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long h = sc.nextLong();
		long w = sc.nextLong();
		long[] area = new long[4];
		Arrays.fill(area, Long.MAX_VALUE);
		// 縦に3分割
		for(int i = 1 ; i < w ; i++) {
			long[] inner = new long[3];
			inner[0] = i * h;
			inner[1] = w / 3 * h;
			inner[2] = (w + 2) / 3 * h;
			long max = Math.max(inner[0], Math.max(inner[1], inner[2]));
			long min = Math.min(inner[0], Math.min(inner[1], inner[2]));
			if(area[0] > max - min) {
				area[0] = max - min;
			}
		}
		// 横に3分割
		for(int i = 1 ; i < h ; i++) {
			long[] inner = new long[3];
			inner[0] = i * w;
			inner[1] = h / 3 * w;
			inner[2] = (h + 2) / 3 * w;
			long max = Math.max(inner[0], Math.max(inner[1], inner[2]));
			long min = Math.min(inner[0], Math.min(inner[1], inner[2]));
			if(area[1] > max - min) {
				area[1] = max - min;
			}
		}
		// 縦半分に分割=>横半分に分割
		for(int i = 1 ; i < w ; i++) {
			long rest = w - i;
			long[] inner = new long[3];
			inner[0] = i * h;
			inner[1] = h / 2 * rest;
			inner[2] = (h + 1) / 2 * rest;
			long max = Math.max(inner[0], Math.max(inner[1], inner[2]));
			long min = Math.min(inner[0], Math.min(inner[1], inner[2]));
			if(area[2] > max - min) {
				area[2] = max - min;
			}
		}
		// 横半分に分割=>縦半分に分割
		for(int i = 1 ; i < h ; i++) {
			long rest = h - i;
			long[] inner = new long[3];
			inner[0] = i * w;
			inner[1] = w / 2 * rest;
			inner[2] = (w + 1) / 2 * rest;
			long max = Math.max(inner[0], Math.max(inner[1], inner[2]));
			long min = Math.min(inner[0], Math.min(inner[1], inner[2]));
			if(area[3] > max - min) {
				area[3] = max - min;
			}
		}
		System.out.println(Arrays.toString(area));
		Arrays.sort(area);
		System.out.println(area[0]);
	}
}