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 PyPy3 (7.3.0) (judge verdict: Accepted)

import math
h,w=map(int,input().split())
ans,cnt=h*w,0
if h%3==0 or w%3==0:
  ans=0
else:
  for i in range(1,h):
    cnt=max((h-i)*(w%2),abs(math.floor(w/2)*(h-i)-w*i),abs(math.ceil(w/2)*(h-i)-w*i))
    ans=min(ans,cnt,h,w)
  for i in range(1,w):
    cnt=max((w-i)*(h%2),abs(math.floor(h/2)*(w-i)-h*i),abs(math.ceil(h/2)*(w-i)-h*i))
    ans=min(ans,cnt,h,w)
print(ans)