Place Pieces on a Grid

Given integers n and m, and an ordered list figures where each element is one of "A", "B", "C", "D", or "E", construct an n x m integer matrix grid.

The grid starts with all values equal to 0.

Each figure has a fixed shape described by a binary matrix, where 1 means the figure occupies that cell and 0 means empty space:

• A = [[1]]
• B = [[1, 1, 1]]
• C = [[1, 1], [1, 1]]
• D = [[1, 0], [1, 1], [1, 0]]
• E = [[0, 1, 0], [1, 1, 1]]

Process the figures in the given order. For the figure at index i:

1. Try all possible top-left placement positions in row-major order: (0, 0), (0, 1), ..., (0, m - 1), (1, 0), ... .
2. A placement is valid if every 1 cell of the figure:

• stays within the bounds of the grid, and
• overlaps only cells that are currently 0.

1. Place the figure at the first valid position.
2. Fill every occupied cell of that placed figure with the value i + 1.
3. If the figure cannot be placed anywhere, skip it and leave the grid unchanged.

Return the final grid.

Figures cannot be rotated or reflected.