Problem 2. (10 points) Suppose you have an augmented binary search tree where at each internal node v, we also store the number of keys of the subtree rooted at v. Complete the following recursive function that will be used to find the number of keys smaller than or equal to the key k in a binary search tree T where the keys are from a totally ordered set (e.g. integers). Use the BST functions T.isExternal(v), T.key(v), T.left Child(v), T.rightChild(v), T.numKeys(v). Your algorithm should have 0(h) time and space complexity where h is the height of the binary search tree. Rank(T,localRoot,k) Input: BST T, node localRoot, key k Output: number of keys smaller than or equal to key k in the subtree of T rooted at localRoot Rank(T.k) Input: BST T, key k Output: number of keys smaller than or equal to key k in T return Rank(T, T.root, k)