Prove the following problem is NL-complete
Let $G'$ be the graph with self-loops added to every vertex. Take $n$ copies $G'_1,G'_2,\ldots,G'_n$ (without the edges) and connect $x \in G'_i$ to $y \in G'_{i+1}$ if $(x,y) \in G'$. The shortest path between $s \in G'_1$ and $t \in G'_n$, if any exists, is now of length exactly $n-1$.