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)

h,w=map(int,input().split())
if h%3==0 or w%3==0:
    print(0)
elif h%2==1 and w%2==1:
    a=max(h,w)//3
    b=min(h,w)
    print(min(abs((a+1)*b-(b//2)*(max(h,w)-a-1)),abs((max(a*b,(b//2+1)*(max(h,w)-a)))-(b//2)*(max(h,w)-a))))
elif h%2==0 and w%2==0:
    a=max(h,w)//3
    b=min(h,w)
    print(min(abs((a+1)*b-(b//2)*(max(h,w)-a-1)),abs((a*b)-(b//2)*(max(h,w)-a))))
elif h%2==0 and h<w:
    a=w//3
    b=h
    print(min(abs((a+1)*b-(b//2)*(max(h,w)-a-1)),abs((a*b)-(b//2)*(max(h,w)-a))))
else:
    a=h//3
    b=w
    print(min(abs((a+1)*b-(b//2)*(h-a-1)),abs((a*b)-(b//2)*(max(h,w)-a))))