Which of the following are true for iterative deepening search, where b is the maximum branching factor and d is the length of a shortest path to a goal state.

(1) If the algorithm finds a path to a goal state it will be a shortest path to a goal state. (2) The algorithm involves repeated calls to depth-limited search where the depth-limit is increased by one each time. (3) The algorithm may not find a path to a goal state even if there is one. (4) The space complexity is bd.