Suppose that youre ready to declare a new major, and your advisor asks you design a course plan. They give you a representation of the departments courses as a DAG, where vertices are courses and edges represent prerequisites. Your task is to decide which courses you want to take, and in what order. Design an algorithm that takes as input the prerequisite DAG along with a proposed set of courses to complete the major, and determines whether there is an order in which those courses can be taken such that all prerequisites will always be satisfied. If such an order exists, you should return it; otherwise return fail.