Suppose there is a strongly connected directed graph G = (V, E) with positive edge weights. It contains a specific edge eo ? E. Modifying Dijkstra's algorithm below, find the shortest paths between all pairs of nodes, with a restriction that all these paths must contain the edge eo. Your algorithm should at the most take O((|V | + |E|)log|V |) time.

dijkstra (G, l, s) Graph G=(V,E), positive edge lengths le : eEE; vertex sEV For all vertices u reachable from s, dist (u) is set to the distance from s tou procedure Input: directed or undirected; Output: for all u EV: dist(u) = oo prev(u) = nil dist(s) = 0 H=makequeue (V) (using dist-values as keys) while H is not empty: u = deleteri n(H) for all edges (u,v)EE: if dist(v) > dist(u)l(u,): dist(u) = dist(u) + 1(mu) prev(v) = u decreasekey(H, v)