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(" "))
 
tmp1 = round(H/3)
tmp2 = round(W/3)
if abs(H-(tmp1*3)) * W < abs(W-(tmp2*3)) * H:
    area = [tmp1 * W]
    A  = H-tmp1
    B  = W
else:
    area = [tmp2 * H]
    A  = W-tmp2
    B  = H
 
tmp1 = round(A/2)
tmp2 = round(B/2)    
 
if abs(A-(tmp1*2)) * B <= abs(B-(tmp2*2)) * A:
    area.extend([tmp1 * B,(A -tmp1) * B])
else:
    area.extend([tmp2 * A,(B -tmp2) * A])
 
print(max(area) - min(area))