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 Ruby (2.3.3) (judge verdict: Accepted)

H, W = gets.split(' ').map(&:to_i)

ans = H * W
(H / 4).upto(H / 2) do |i|
	a = W * i
	if (H - i) % 2 == 0 || W % 2 == 0
		b, c = (H - i) * W / 2
		ans = [ans, (a - b).abs].min
	else
		b = (H - i) * (W + 1) / 2
		c = (H - i) * (W - 1) / 2
		ans = [ans, [a, b, c].max - [a, b, c].min].min
		b = (H - i + 1) / 2 * W 
		c = (H - i - 1) / 2 * W
		ans = [ans, [a, b, c].max - [a, b, c].min].min
	end
end
H, W = W, H
(H / 4).upto(H / 2) do |i|
	a = W * i
	if (H - i) % 2 == 0 || W % 2 == 0
		b, c = (H - i) * W / 2
		ans = [ans, (a - b).abs].min
	else
		b = (H - i) * (W + 1) / 2
		c = (H - i) * (W - 1) / 2
		ans = [ans, [a, b, c].max - [a, b, c].min].min
		b = (H - i + 1) / 2 * W 
		c = (H - i - 1) / 2 * W
		ans = [ans, [a, b, c].max - [a, b, c].min].min
	end
end
puts ans