# Home

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