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 Python (3.4.3) (judge verdict: Accepted)

def sp(n):
  a = n // 3
  b = (n - a) // 2
  c = n -a -b
  return a,b,c

def ceil(x, y):
  return (x -1) // y + 1

def tatedake_diff(h, w):
  a,b,c = sp(h)
  s1 = (c-a) * w
  a,b,c = sp(w)
  s2 = (c-a) * h
  return min(s1, s2)

def tateyoko_diff(h, w):
  a,b,c = sp(h)
  s1 = (c * w)
  s2 = (h - c) * (w // 2)
  s3 = (h - c) * ceil(w, 2)
  r1 = max(s1,s2,s3) - min(s1,s2,s3)
  s1 = (a * w)
  s2 = (h - a) * (w // 2)
  s3 = (h - a) * ceil(w, 2)
  r2 = max(s1,s2,s3) - min(s1,s2,s3)
  return min(r1,r2)
  
H, W = map(int, input().split())
if H % 3 == 0 or W % 3 == 0:
  ans = 0
else:
  ans = min(tatedake_diff(H, W), tateyoko_diff(H, W), tateyoko_diff(W, H))
print(ans)