We define an augmented binary search tree to be a binary search tree where each node v in the tree also stores the value size[v], which is equal to the number of nodes in the subtree rooted at v. (a) Show that a rotation in an augmented binary tree can be performed in constant time. (b) Describe an algorithm SPLAYSELECT(k), 1 k n, that selects the kth smallest item in an augmented splay tree with n nodes in O (log n) amortized time. Justify your algorithm and its running time