Anna has just won a contest that allows her to take n pieces of candy out of a candy store for free. Anna is old enough to realize that some candy is expensive, while other candy is relatively cheap, costing much less. The jars of candy are numbered 0, 1, . . ., m−1, so that jar j has n_j pieces in it, with a price of c_j per piece. Design an O(n+m)-time algorithm that allows Anna to maximize the value of the pieces of candy she takes for her winnings. Show that your algorithm produces the maximum value for Anna.