Let M be the PDA with states Q = {q0, q1, and q2}, final states F = {q1, q2} and transition function

(q0, a, ) = {[q0, A]}

(q0, , ) = {[q1, ]}

(q0, b, A) = {[q2, ]}

(q1, , A) = {[q1, ]}

(q2, b, A) = {[q2, ]}

(q2, , A) = {[q2, ]}

Construct a grammar G such that L(G) = L(M) where M is the PDA. Then show that the word aaaabb is generated by G.