100622: [AtCoder]ABC062 C - Chocolate Bar

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