Chess puzzle

Requirements

Find the number of unique arrangements of pieces on a chessboard of a given size (WIDTHxHEIGHT) so that the pieces do not threaten each other.

Examples

1. Chessboard of size 3x3 and pieces: 2 kings, 1 rook – 4 unique solutions.
2. Chessboard of size 4x4 and pieces: 2 rooks, 4 knights – 8 unique solutions.