3. (16 pts.] Consider the SUCCESSOR function (Algorithm 4) for a general linked-structured BST implementation for a sorted map ADT. It takes as input a node w in a general BST and outputs its successor node in the BST, that is, the node whose key immediately follows the key w.key of node w, if any otherwise it outputs NULL. It uses two auxiliary functions, FIRSTLEFT ANCESTOR and FLOOR ENTRYNODE. Algorithm 4 SUCCESSOR (W) 1: if w = NULL then return w 2: if w.right = NULL then return FIRSTLEFTANCESTOR(0) 3: return FLOORENTRYNODE(w.right) (a) Write an algorithm, using pseudocode, for the function FIRSTLEFTANCESTOR, which takes as input a node w in the BST and outputs the first ancestor u of w in the BST such that w is the ceiling entry node of the left subtree w.left of u, that is, the key w.key of w is the largest in the left subtree of u, so that, w is the predecessor of u in the BST; it outputs NULL if no such ancestor exists, or if the subtree is empty. The algorithm should run in time that is linear in the depth of node w in the BST, and use a constant amount of space