You must buy one unit at each of n times, at a Uniform(a, b) market price you see first or from a broker at fixed price p, at most k times. Compute the expected optimal cost.

You must buy n units, one at each of n distinct times. At each time the market price is an independent Uniform(a, b) draw seen before you decide; you either buy at that price or use a broker who sells at a fixed price p, but only at most k times in total. Given n, a, b, k and p, return the expected total price you pay (execution cost) under optimal play.