(computability and complexity): prove well: if there exists an algorithm that can decide language ACYCLIC in polynomial time, then there's an algorithm that returns a set of k edges, so that the graph that is obtained from deleting those k edges is without circles, in polynomial time. this algorithm gets as an input a directed graph G and a natural k; if there's no set of k edges as required, it returns "no", else, if there are k edges as needed, the algorithm returns a list of the k edges, so that the graph that is obtained from erasing those k edges is without any circles. note: it is allowed to use the algorithm that decides the languages ACYCLIC - but it CANNOT use any other NP-COMPLETE algorithms. its running time must be polynomial in regards to input size. explain well

(the question is about a directed graph, not weighted).

please make the proof academic level. thank you very much