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)

ans = h * w

def min(a,b)
  a < b ? a : b
end

def max(a,b)
  a > b ? a : b
end



# 分割は4パターンということがわかる
# HとWの大きさを入れ替えたりすれば同じやりかたでいけるので2パターンについて考察する
# たて3つに分割した場合でも、T時の場合でも一番上の大きさは同じ

#  たて
1.upto(h-1) do |i|
  s_1 = i * w
  s_2 = (w/2) * (h-i)
  s_3 = (w-w/2)* (h-i)

  s = [s_1, s_2, s_3]
  ans = min(s.max - s.min, ans)


  s_2 = ((h-i)/2) * w
  s_3 = ((h-i)-(h-i)/2)* w

  s = [s_1, s_2, s_3]


  ans = min(s.max - s.min, ans)
end



# よこ
1.upto(w-1) do |j|
  s_1 = h * j
  s_2 = (h/2) * (w-j)
  s_3 = (h-h/2)* (w-j)

  s = [s_1, s_2, s_3]
  ans = min(s.max - s.min, ans)

  s_2 = ((w-j)/2) * h
  s_3 = ((w-j)-(w-j)/2)* h

  s = [s_1, s_2, s_3]


  ans = min(s.max - s.min, ans)
end

p ans