2. This problem is concerned with range queries (a topic discussed in class) on a normal binary search tree T whose keys are real numbers. The range queries are generalizations of the normal search(key) operation. The range of a range query on T is an interval specified by a pair [a, ar] of query input, where x and z, are real numbers and a r. Note that the input numbers ay and z, that define a query range need not be keys stored in the tree T. You are asked to design a binary search tree T that supports the normal search, insert, and delete operations, each in O(h) time, where h is the height of T. In addition, your binary search tree T must also support the following two range queries, each in O(h) time. (a) range-count(a, a,): Given any range [, ,] for a range query on T, report the number of keys of T in the range of [, 2]. (15 points) (b) range-sum(x, x): Given any range [a, r] for a range query on T, report the sum of keys of T in the range of (a, a,). (15 points) Note: You are asked to present the design of your data structure and the two operations in (a) and (b).