Given a set S of n unsorted, distinct real numbers and an integer k [2,n/2], your task here is to find the k-1 numbers $ < $ < < Sk-1 in S that partition the set S into k equal-sized subsets S2 (to within 1 in size differences) S1, S2,, Sk, such that all items x in S have x s, all items x in S have s < x s2, and so on, and in the end all items x in Sk have Sk-1 < x. Note that this is the median-finding problem when k = 2. Here k is a given parameter and is not considered as a constant. (a) Suppose for simplicity that k is a power of 2. Design and analyze an algorithm to carry out the task in O(n log k) worst-case time. (13 points) (b) Now consider the general case where k is an arbitrary integer in [2, n/2]. Design and analyze an algorithm to carry out the task in O(n log k) worst-case time. (Hint: Use your algorithm in part (a) as a subroutine.) (12 points)