CSES 1673 High Score - Two-Way Reachability

A negative cycle only causes infinite score if you can use it on a path from $1$ to $n$. The cycle must be both reachable from the source and able to reach the destination. Run BFS from node $1$ to find all reachable nodes. Run BFS on the reversed graph from node $n$ to find all nodes that can reach $n$.

A node can reach $n$ in the original graph if $n$ can reach it in the reversed graph. If a negative cycle node is both reachable from $1$ and can reach $n$, output $-1$. Otherwise, the cycle is irrelevant, and you output the negated shortest distance.