Consider a state space where the start state is number $-1$ and each state k has three successors: number $2$k$,2$k$+1,$ and k$+2.$

a$.$ Draw the portion of the state space for states $-1$ to $15.$

b$.$ Suppose the goal state is $21,$ List the order in which nodes will be visited for breadth$-$first search, depth$-$limited search with limit $3,$ and iterative deepening search. When generating children of a node, list the order of the generated nodes.