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.chomp.split.map(&:to_i)

if H % 3 == 0 || W % 3 == 0
  p 0
  exit
end

def harf(h, w)
  if h % 2 == 0 || w % 2 == 0
    s = (h * w) / 2
    [s, s]
  else
    h, w = w, h if w > h
    hh = h / 2
    [hh * w, (h - hh) * w]
  end
end

ans = 10 ** 10
h = H
w = W
1.upto(h-1).each do |hh|
  arr = harf((h-hh),w).push(hh*w).sort
  s = arr.last - arr.first
  ans = s if s < ans
end
1.upto(w-1).each do |ww|
  arr = harf((w-ww),h).push(h*ww).sort
  s = arr.last - arr.first
  ans = s if s < ans
end
p ans