a$)$ Find a regular grammar that generates the following language on $=\{a,b,c\}$ :

$L=\{a^n{b}^m{c}^k$:$n2,m0,k3\}$

b$)$ Convert the NFA defined by

$(q_0,a)=\{q_0,q_1\},(q_1,(b))=\{q_1,q_2\},(q_2,a)=\{q_2\},(q_1,)=\{q_1,q_2\}$

with initial state $q_0$ and final state $q_2$ into an equivalent DFA.