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 (2.7.6) (judge verdict: Accepted)

x, y = map(int, raw_input().split())

if x % 3 == 0 or y % 3 == 0:
	print 0
else:
	m = 10000000
	for i in range(1, x):
		j = y / 2
		s1 = y * i
		s2 = (x - i) * j
		s3 = (x - i) * (y - j)
		l = [s1, s2, s3]
		l.sort()
		if l[-1] - l[0] < m:
			m = l[-1] - l[0]
			# ix = i
			# ij = j
	# print m
	x, y = y, x
	for i in range(1, x):
		j = y / 2
		s1 = y * i
		s2 = (x - i) * j
		s3 = (x - i) * (y - j)
		l = [s1, s2, s3]
		l.sort()
		if l[-1] - l[0] < m:
			m = l[-1] - l[0]
	if m > x:
		m = x
	if m > y:
		m = y
	print m