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: Wrong Answer)

h,w=gets.split.map(&:to_i)
ans=Array.new(6)
if h%3==0 || w%3==0
	answer=0
else
	k=h#とする
	mul=h*w
	trip=mul/3 #6
	for i in 0..2
		green=(trip/h+i)*h
		
		blue=(w-(trip/h+i))*(h/2) 
		
		red=mul-green-blue
		if green==0 || blue==0 || red==0
			next
		end
		num= (green-blue).abs > (green-red).abs ? blue : red
		
		ans[i]=(green-num).abs
	end
	for i in 0..2
		green=(trip/w+i)*w
		
		blue=(h-(trip/w+i))*(w/2)
		
		red=mul-green-blue
		if green==0 || blue==0 || red==0
			next
		end
		num= (green-blue).abs > (green-red).abs ? blue : red
		ans[3+i]=(green-num).abs
	end
	ans.compact!
	answer=ans.min
end

puts answer