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: Wrong Answer)

n,m = map(int,input().split())
if n*m % 3 == 0:
  print("0")
elif n == 1 or m == 1:
  print("1")
else:
  a = n//3+1
  b = m//3+1
  c = a*m-float(n*m/3)
  d = b*n-float(n*m/3)
  e = c-m
  f = d-n
  if c<d:
    smax = a*m
    if m % 2 == 1:
      smin = (n-a)*(m-1)/2
    else:
      smin = (n-a)*(m/2)
  else:
    smax = b*n
    if n % 2 == 1:
      smin = (m-b)*(n-1)/2
    else:
      smin = (m-b)*(n/2)
  if f<e:
    smin2 = smax - m
    if m % 2 == 1:
      smax2 = (n-a+1)*(m+1)/2
    else:
      smax2 = (n-a+1)*(m/2)
  else:
    smin2 = smax - n
    if m % 2 == 1:
      smax2 = (m-b+1)*(n+1)/2
    else:
      smax2 = (m-b+1)*n/2
  print (min(int(smax-smin),int(smax2-smin2)))