Another Brick in the Wall

Alice likes building toy walls. She has a lot of $1 \times 2$ bricks and a limited supply of $1 \times 3$ bricks. Both types of bricks have a height of 1 and can not be rotated.

Alice is going to build a one unit thick wall of length $l$ and height $h$ out of these bricks. A wall is solid if there are no seams directly above another seam.

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

Help Alice determine the minimum number of $1 \times 3$ bricks required to build a solid wall of length $l$ and height $h$.

The only line contains two integers $l$ and $h$, denoting 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 required to build a solid $l \times h$ wall.

It can be shown that it is always possible to build a solid wall of length $l$ and height $h$.