Minimum Weighted Subgraph With the Required Paths

Given a weighted directed graph and nodes src1, src2, and dest, find the minimum total edge weight of a subgraph that allows both src1 and src2 to reach dest; the core challenge is combining shortest-path costs (from src1 and src2 and toward dest) to choose an optimal meeting/merge node that minimizes the total sum, or return -1 if no such routes exist.