Modify Graph Edge Weights

Given an undirected weighted graph where some edges have weight -1 (modifiable) and others are fixed, assign positive integer weights (in [1, 2e9]) to the -1 edges so that the shortest-path distance from source to destination equals a given target, or report impossibility. The core challenge is finding weight assignments that exactly match the target shortest-path length while respecting the fixed edges and shortest-path structure.