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.*;

public class Main {
	
	/*
	 * default function
	 * */	
	int ni() {
		return cin.nextInt();
	}
	
	long nl() {
		return cin.nextLong();
	}
	
	String line() {
		return cin.nextLine();
	}
	
	void println(String str) {	
		System.out.println(str);
	}
	
	void print(String str) {
		System.out.print(str);
	}
	
	/*
	 * default variable
	 */
	
	static final int MOD = 1000000007;
	
	Scanner cin = new Scanner(System.in);	
	String  output;
	
	public static void main(String[] args) {			
		new Main().run();						
	}
	/* default above */
		
	public void run() {
			
		input();
		/* 
		 * start
		 */	
		
		int res = solve();
		
		/*
		 * finish
		 */
		
		output = res +"";
		println(output);
			
	}
	/* 
	 * define variable
	 */
	
	int H, W;
	
	void input() {
		H = ni();
		W = ni();
		
		if (W > H) {
			W = H + W;
			H = W - H;
			W = W - H;
		}
	}
	
	int solve() {
		
		if (H % 3 == 0 || W % 3 == 0) {
			return 0;
		}
		
		if (W == 2) {
			return 1;
		}
		
		return cal(H, W);		
	}
	
	int cal(long h, long w) {
		
		long res = Long.MAX_VALUE;
		
		
		long a[] = new long[3];
		a[0] = (h / 2) * w;
		a[1] = (h - h/2) * (w / 2);
		a[2] = (h - h/2) * (w - w/2);
		Arrays.sort(a);
		res = Math.min(res, a[2] - a[0]);
		
		
		a[0] = (h/3) * w;
		a[1] = (h - h/3) * (w/2);
		a[2] = (h - h/3) * (w - w/2);
		Arrays.sort(a);
		res = Math.min(res, a[2] - a[0]);
		
		
		return (int)res;
	}
	
	
}