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 = h * w
if h % 3 == 0 || w % 3 == 0 then
  ans = 0
elsif h >= w
  1.upto(h/2) { |y|
    arr = [y*w, (h-y)*(w/2), (h-y)*(w-w/2)]
    s = arr.max - arr.min
    ans = s  if ans > s
    #print "y:", y, " x:", w/2, " ", arr, " s:", s, "\n"
  }
else
  1.upto(w/2) { |x|
    arr = [h*x, (h/2)*(w-x), (h-h/2)*(w-x)]
    s = arr.max - arr.min
    ans = s  if ans > s
    #print "y:", h/2, " x:", x, " ", arr, " s:", s, "\n"
  }
end
puts ans