Shortest path in combinatorial optimization

Consider a digraph D = (V, A) with two distinct vertices s and t. (a) Let F denote the set of edges in A which appear in some shortest s-t path (in terms of the number of edges) in D. Give an algorithm to output F in O(|V| + |A|) time. (b) Give an efficient algorithm to find an inclusion-wise maximal (not necessarily) edge-disjoint shortest s-t paths in D in O(|V| + |A|) time