Exercise 1. DIVIDE-AND-CONQUER. Design a divide-and-conquer style algorithm to compute the 2" inner products s.X, where s is a given fixed vector of n integers, n is a power of two (only if you find this more convenient), and x takes all values in {-1,1}". Using the obvious one-to-one map between {0, ..., 21 1} and {-1,1}", your output should be an array of 2" values where the i-the element of the array holds s . x for the unique x that corresponds to i. Using only integer artithmetic (addition, subtraction, mod, division, multiplication) in a RAM model, make sure that the overall complexity is 0(2")