The graph described in the problem statement is a hypergraph. When solving the shortest path problem on a hypergraph, we can convert it to a "normal" undirected graph by simply connecting all pairs of nodes (stations) on the same hyperedge (hypertube) with undirected edges. This results in a graph with a total of ~N~ nodes and ~M \times K \times (K-1)/2~ edges. A simple breadth-first search applied to this graph is then a solution, ignoring time and memory constraints.

However, the constraints prevent such a solution from obtaining all points. The most elegant way to speed up the solution is adding a new node for each hypertube, connecting it with undirected edges to all stations connected to the corresponding hypertube. Such a graph has ~N+M~ nodes and ~M \times K~ edges. A breadth-first search applied to this graph yields the solution ~2X-1~, where ~X~ is the number of stations on the shortest path from station ~1~ to station ~N~.