Decide reachability with buses and limited walking

You are given: ( 1) a start point (xs, ys), ( 2) an end point (xe, ye), ( 3) an integer K, and ( 4) an undirected graph of bus stations where each node has integer coordinates (xi, yi) and edges indicate bidirectional bus routes. Walking uses Manhattan distance d((x1, y 1), (x2, y 2)) = |x1 − x2| + |y1 − y2|. Riding a bus along any sequence of connected stations costs zero walking distance. You may: (a) walk from the start to any station (s), ride buses across the graph, then walk from some station to the end; or (b) walk directly from start to end. Determine whether there exists a strategy whose total walking distance is ≤ K. Design an algorithm, state and justify its correctness, analyze time/space complexity, and implement a function returning true/false.