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$.001110$