2. (20 points) Throughout this problem, assume n and k are each some power of 2 As a variation of merge sort, suppose we try the following . We are given an array of n integers . We divide the array into 4 parts of equal size Each of the 4 parts is sorted separately. . The 4 resulting sorted piles are then merged into a single sorted result of n integers (a) (4 points) Below, write the recurrence for T(n) that describes the time taken to carry out the above algorithm (b) (4 points) Based on the master method, what is the solution to your recurrence? (c) (4 points) Now suppose we generalize this approach and create k parts from the n integers. Above, k 4, but now k is some constant power of 2, 1