Given a set T of numbers (represented in an array A[1..n]), a sum s, and a non-negative integer k, our task is to design an algorithm to identify a subset of numbers in T, with size k, such that the sum of the numbers in the subset equals s, or report that such a subset does not exist.

(a) Design a recursive algorithm to enumerate all subsets of T with size k and analyze its time complexity. If T = {4, -2, 3} and k = 2, the output would be the list as follows (can be in any order):

4

-2

3

4, -2

4, 3

-2, 3

(b) Based on your algorithm in (a), design an algorithm to solve the above problem and analyze the time complexity of your algorithm.