Apply the Cartesian product construction from class to construct a state diagram of a DFA for the following language:

L = {w {a, b} | w has an odd number of as and w contains the substring bb}.

Recall that the Cartesian product construction is summarized in the proof of Theorem 1.25; see also the footnote at the bottom of page 46 that relates to the intersection operation. Remove unreachable states (if any), but do not otherwise simplify your DFA. You only need to show your final DFA.