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 $N$.