Another Brick in the Wall

Alice likes building toy walls. She has many $1 \times 2$ bricks and a limited supply of $1 \times 3$ bricks. Both types of bricks are 1 unit high and cannot be rotated.

Alice builds a wall one unit thick, with length $l$ and height $h$, using these bricks. A wall is solid if no seam lies directly above another seam.

Good seam placement	Bad seam placement	Solid $7 \times 4$ wall

Find the minimum number of $1 \times 3$ bricks needed to build a solid wall of length $l$ and height $h$.

The only line contains two integers $l$ and $h$, the length and the height of the wall ($5 \le l \le 1000$; $2 \le h \le 1000$).

Print the minimum number of $1 \times 3$ bricks needed to build a solid $l \times h$ wall.

It is always possible to build a solid wall of length $l$ and height $h$.