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)

def max(a, b, c)
  a < b ? (b < c ? c : b) : (a < c ? c : a)
end
def min(a, b, c)
  a > b ? (b > c ? c : b) : (a > c ? c : a)
end
def cdiv(a, b)
  (a + b - 1) / b
end

H, W = gets.split.map(&:to_i)



results = []
if H == 2

elsif H % 3 == 0
  results.push(0)
else
  results.push(((H / 3 + 1) * W) - ((H / 3) * W))
end

if W == 2

elsif W % 3 == 0
  results.push(0)
else
  results.push(((W / 3 + 1) * H) - ((W / 3) * H))
end

(cdiv(H, 4)..cdiv(H, 2)).each do |h|
  pieces = [h * W]
  pieces.push (H - h) * (W / 2)
  pieces.push (H - h) * ((W + 1) / 2)
  results.push max(pieces[0], pieces[1], pieces[2]) - min(pieces[0], pieces[1], pieces[2])
end

(cdiv(W, 4)..cdiv(W, 2)).each do |h|
  pieces = [h * H]
  pieces.push (W - h) * (H / 2)
  pieces.push (W - h) * ((H + 1) / 2)
  results.push max(pieces[0], pieces[1], pieces[2]) - min(pieces[0], pieces[1], pieces[2])
end

puts results.min