Consider the regular language L accepted by the following DFA M$.$

The proof of the pumping lemma in the textbook indicate that one of the pumping length is p $=4$ for L$,$ since M has $4$ states. For each of the following string w$,$ determine if w is in L and $|$w$|>=$ p$.$ If so$,$ find x$,$ y and z$,$ where w $=$ xyz and conditions $($i$)($iii$)$ in the pumping lemma hold.

a$.100101$

b$.001110$