Stacking Bars

Simulate bars of lumber being dropped onto a narrow shelf, where full rows are cleared.

The shelf has width columns (numbered from 0, left to right) and room for height rows. Row 1 is the floor. Each bar is a pair [column, length]: a horizontal bar that covers length consecutive columns starting at column, one cell thick. Bars are dropped one at a time, in order. Bars only move straight down, never sideways, and cells are never pushed around by later bars.

For each bar:

1. Validity. If length < 1, column < 0, or column + length > width, the bar does not fit on the shelf. Ignore it completely (do not clip it).
2. Landing. The bar falls until it rests on something. It comes to rest in row 1 + h, where h is the largest number such that some column the bar covers has a filled cell in row h (and h = 0 if none of its columns has any filled cell). Gaps underneath an overhang stay empty and can never be filled again by a later bar, because bars are blocked by the highest filled cell in each column.
3. Height limit. If the landing row is above row height, the bar does not fit: ignore it. The shelf is unchanged.
4. Placement and clearing. Fill the bar's cells in its landing row. If that row is now completely filled, remove it: every row above it moves down by one row as a whole (cells keep their column and their gaps; nothing falls into the empty cells under overhangs).

Input: width and height, integers, and bars, a list of [column, length] pairs.

Output: the final shelf as a list of strings, one per row from the top row down to the floor row, with # for a filled cell and . for an empty one. Include rows only up to the highest row that has a filled cell; if the shelf is empty return [].