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)


def min(ans, arr)
  d = arr.minmax.inject(&:-).abs
  return ((d < ans) ? d : ans)
end

def solver(h, w)
  ans = 1e11
  (h + 1).times do |i|
    sa = w * i
    # tate
    wi = w / 2
    sb = (h - i) * wi
    sc = (h - i) * (w - wi)
    ans = min(ans, [sa, sb, sc])
    # yoko
    hi = (h - i) / 2
    sb = hi * w
    sc = (h - hi - i) * w
    ans = min(ans, [sa, sb, sc])
  end
  ans
end

# 1
# (h + 1).times do |i|
#   sa = w * i
#   # tate
#   wi = w / 2
#   sb = (h - i) * wi
#   sc = (h - i) * (w - wi)
#   ans = min(ans, [sa, sb, sc])
#   # yoko
#   hi = (h - i) / 2
#   sb = hi * w
#   sc = (h - hi - i) * w
#   ans = min(ans, [sa, sb, sc])
# end
# # 2
# (w + 1).times do |i|
#   sa = h * i
#   # yoko
#   hi = h / 2
#   sb = (w - i) * hi
#   sc = (w - i) * (h - hi)
#   ans = min(ans, [sa, sb, sc])
#   # tate
#   wi = (w - i) / 2
#   sb = wi * h
#   sc = (w - wi - i) * h
#   ans = min(ans, [sa, sb, sc])
# end
p [solver(h, w), solver(w, h)].min