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())
deference=H*W
a=0
b=0
for i in range(W-1):
    a=H*(i+1)
    b=H//2*(W-i-1)
    if deference>max(a, b, H*W-a-b)-min(a, b, H*W-a-b):
        deference=max(a, b, H*W-a-b)-min(a, b, H*W-a-b)
for i in range(H-1):
    a=W*(i+1)
    b=W//2*(H-i-1)
    if deference>max(a, b, H*W-a-b)-min(a, b, H*W-a-b):
        deference=max(a, b, H*W-a-b)-min(a, b, H*W-a-b)
for i in range(W-2):
    a=H*(i+1)
    b=H*((W-i-1)//2)
    if deference>max(a, b, H*W-a-b)-min(a, b, H*W-a-b):
        deference=max(a, b, H*W-a-b)-min(a, b, H*W-a-b)
for i in range(H-2):
    a=W*(i+1)
    b=W*((H-i-1)//2)
    if deference>max(a, b, H*W-a-b)-min(a, b, H*W-a-b):
        deference=max(a, b, H*W-a-b)-min(a, b, H*W-a-b)
print(deference)