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 = map(int, input().split())

if not H % 3 or not W % 3:
	print(0)
	exit()

#min_p = None
min_diff = 2 ** 31 - 1

def func(A, B):
	global min_p
	global min_diff
	for a in range(1, A + 1):
		area = []
		area += [a * B]
		area += [(A - a) * (B // 2)]
		area += [(A - a) * (B - B // 2)]
		if max(area) - min(area) < min_diff:
			min_diff = max(area) - min(area)
			#min_p = [A, B, a, area]

func(H, W)
func(W, H)

#print(min_p)
print(min_diff)