Altenative solution(The Dirty Path)

"At least one “#” was added
(b’, 0) → (b’, b’) → (b’, 2 * b’) → (2 * b’, 3 * b’) → … → (b, 0) "

I dont understand why if a ‘.’ is placed after a ‘#’ dn the state goes from (b’,0 ) to (b’,b’) and not (b’,0 ) to (0,b’)?

( The first parameter of the state is the number of ways to reach the 2nd last charactr until now, and the 2nd parametr is the number of ways to reach the last charactr untl now, have I got anything wrong here?)

Can you describe your approach in more detail - I do not understand where is the problem…