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())
ans = float("inf")

Hh = [H//2,H//2+1]
Wh = [W//2,W//2+1]
Ht = [H//3,H//3+1]
Wt = [W//3,W//3+1]

for i in Ht:
  for j in Ht:
    k = H -i -j
    ans = min(ans,W*(max(i,j,k)-min(i,j,k)))
for i in Wt:
  for j in Wt:
    k = W -i -j
    ans = min(ans,H*(max(i,j,k)-min(i,j,k)))

for i in Ht:
  b = H-i
  for j in Wh:
    k = W-j
    ans = min(ans, max(W*i,b*j,b*k)-min(W*i,b*j,b*k))
for i in Wt:
  b = W-i
  for j in Hh:
    k = H-j
    ans = min(ans, max(H*i,b*j,b*k)-min(H*i,b*j,b*k))
###
print(ans)