Recall the (worst-case) linear-time divide-and-conquer algorithm for finding the kth smallest of n reals, where we used groups of size 5. Suppose that we use the same algorithm but with groups of size g for some positive integer constant g. Derive the recurrence relation for this algorithm as a function of n and g. (Consider separately the case where g is even and where it is odd.) Based on your recurrences, determine the smallest integer g for which the algorithm runs in linear time and justify your answer.