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)

h,w = map(int,input().split())
if (h%3 == 0) or (w%3 == 0):
  print(0)
else:
  ans = h*w
  for i in range(1,max(h,w)//2 + 1):
    a = min(h,w)*i
    b = (max(h,w)-i)*(min(h,w)//2)
    if min(h,w)%2 != 0:
      c = (max(h,w)-i)*(min(h,w)//2 + 1)
    else:
      c = b
    kari = max(a,b,c)-min(a,b,c)
    if ans > kari:
      ans = kari
  ans3 = h*w
  for i in range(1,min(h,w)//2 + 1):
    a = max(h,w)*i
    b = (min(h,w)-i)*(max(h,w)//2)
    if max(h,w)%2 != 0:
      c = (min(h,w)-i)*(max(h,w)//2 + 1)
    else:
      c = b
    kari = max(a,b,c)-min(a,b,c)
    if ans3 > kari:
      ans3 = kari
  ans2 = ((max(h,w)//3 + 1)*min(h,w))-((max(h,w)//3)*min(h,w))
  print(min(ans,ans2,ans3))