Network Recovery Pathways

You are given a directed acyclic graph with n nodes numbered from 0 to n-1. Each directed edge has an associated repair cost. Some nodes may not be accessible (offline), but node 0 and node n-1 are always available.

We want to travel from node 0 to node n-1. A path is considered valid if:

1. Every node on the path (except the endpoints) is online.

2. The sum of all edge costs on this path does not exceed the value k.

For each valid path, define its value as the smallest edge cost in that path.
Return the maximum such value among all valid paths.
If no valid path exists, return -1.