You’re a construction engineer tasked with building a new transit center for a large city. the design for the center calls for a t-foot-long steel beam for integer t > 0. your supplier can provide you with an unlimited number of steel beams of integer lengths 0 < c1 < . . < ck feet. you can weld as many beams as you like together; if you weld together an a-foot beam and a b-foot beam you’ll have an (a + b)-foot beam. unfortunately, every weld increases the chance that the beam might break, so you want as few as possible. your task is to design an algorithm which outputs how many beams of each length you need to obtain a t-foot beam with the