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: Accepted)

import java.util.*;
 
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int H = sc.nextInt();
		int W = sc.nextInt();
		if(H%3==0 || W%3==0){
			System.out.println(0);
			return;
		}
		
		int h1 = H/2;
		int h2;
		if( H%2==0 ){
			h2 = h1;
		}else{
			h2 = h1+1;
		}
		int w1 = W/2;
		int w2;
		if( W%2==0 ){
			w2 = w1;
		}else{
			w2 = w1+1;
		}
		
		
		long a1 = W/3;
		if(a1==0)a1++;
		long a2 = (W-a1)*h1;
		long a3 = (W-a1)*h2;
		long cur = Math.max(a1*H,Math.max(a2, a3)) - Math.min(a1*H, Math.min(a2,a3));
		a1++;
		if(a1 < W){
			a2 = (W-a1)*h1;
			a3 = (W-a1)*h2;
			cur = Math.min(cur, Math.max(a1*H,Math.max(a2, a3)) - Math.min(a1*H, Math.min(a2,a3)));
		}
		
		a1 = H/3;
		if(a1==0)a1++;
		a2 = (H-a1)*w1;
		a3 = (H-a1)*w2;
		cur = Math.min(cur, Math.max(a1*W,Math.max(a2, a3)) - Math.min(a1*W, Math.min(a2,a3)));
		a1++;
		if(a1 < H){
			a2 = (H-a1)*w1;
			a3 = (H-a1)*w2;
			cur = Math.min(cur, Math.max(a1*W,Math.max(a2, a3)) - Math.min(a1*W, Math.min(a2,a3)));
		}
		
		cur = Math.min(cur, Math.min(H, W));
		System.out.println(cur);
		return;
	}
}