$)$ Construct an NFA M over the alphabet $\{$a$,$ b$\}$ such that the language accepted by M consists of strings in which the last but one symbol is $$a$.$ Make sure M exhibits the two features that a DFA can not exhibit$(1.$ Multiple transitions on the

same state and symbol $2.$ Missing transitions on some states and symbols.$)$ Show the transition diagram of your NFA. On paper

Show a successful execution sequence for the input string babaa. You can show your result by writing

an alternating sequence of states and input symbols so that it represents a sequence of transitions of M

Show three unsuccessful executions of M on the input aababab.