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)
m=h*w
a=h/3*w
b=(h-h/3)/2*w
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
b=(h-h/3)*(w/2)
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
a=(h/3+1)*w
b=(h-h/3-1)/2*w
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
b=(h-h/3-1)*(w/2)
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
a=w/3*h
b=(w-w/3)/2*h
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
b=(w-w/3)*(h/2)
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
a=(w/3+1)*h
b=(w-w/3-1)/2*h
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
b=(w-w/3-1)*(h/2)
c=h*w-a-b
if [a,b,c].max-[a,b,c].min<m
  m=[a,b,c].max-[a,b,c].min
end
puts m