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 Python (3.4.3) (judge verdict: Wrong Answer)

h,w = (int(i) for i in input().split())
if h%3==0 or w%3==0:
	answer = 0
elif h==2 or w==2:
	answer = 1
else:
	h1,w1 = (h-h%3)//3,(w-w%2)//2
	x = [w*h1,(h-h1)*(w-w1),(h-h1)*w1]
	y = [w*(h1+1),(h-h1-1)*w1,(h-h1-1)*(w-w1)]
	a = min(max(x)-min(x),max(y)-min(y))
	w2,h2 = (w-w%3)//3,(h-h%2)//2
	x2 = [h*w2,(w-w2)*(h-h2),(w-w2)*h2]
	y2 = [h*(w2+1),(w-w2-1)*h2,(w-w2-1)*(h-h2)]
	b = min(max(x2)-min(x2),max(y2)-min(y2))
	answer = min(a,b)
print(answer)