Bigger Sokoban 40k

Sokoban is a famous puzzle game. The player moves around in an $N \times M$ grid and pushes $1 \times 1$ boxes onto $1 \times 1$ storage locations.

Bigger Sokoban is a variation of Sokoban where the boxes and storage locations are larger than $1 \times 1$. This problem uses $2 \times 2$ for both.

The rules of Bigger Sokoban are the same as Sokoban. Each square in the grid is either empty or a wall. Some $2 \times 2$ areas of empty squares each contain one $2 \times 2$ box, and some $2 \times 2$ areas of empty squares are each marked as a $2 \times 2$ storage location.

The player moves up, down, left, or right to adjacent empty squares. The player cannot pass through walls, boxes, or the outside of the grid. If the player tries to move into a box, the box is pushed one square in that direction. A box cannot be pushed into another box, a wall, or outside the grid, and boxes cannot be pulled. The number of boxes equals the number of storage locations. The puzzle is solved when every box is on a storage location.

Your task is to build a Bigger Sokoban grid that requires at least 40,000 moves to solve. The grid must satisfy these constraints:

• $1 \leq N, \; M, \; N+M \leq 100$.
• The grid contains exactly one box and one storage location.
• The player, the box, and the storage location do not overlap.

There is no input for this problem.

Print two space-separated integers $N$ and $M$ on the first line. They give the size of the grid.

On each of the following $N$ lines, print a string of length $M$ that describes one row of the grid. Each string consists of ., #, P, B, and S, which mean an empty square, a wall, the player, a box, and a storage location, respectively.

The grid must contain exactly one P, exactly four B, and exactly four S. The B characters must form one $2 \times 2$ square, and the S characters must form one $2 \times 2$ square. The grid must be solvable.