Consider a state space where the start state is number 2 and each state k has two successors: numbers 2k and 2k+1 a. Draw a State Space Graph that generates successors up to number 23. b. Does your graph include every integer between 2 and 23 ? c. Suppose the goal state is 20. List the order in which nodes will be visited for breadthfirst search, depth-limited search with depth limit 3, and iterative deepening search. [hint: root is depth 0]. d. How well would bidirectional search work on this problem? What is the branching factor in each direction of the bidirectional search