).* Path $\pi_\mathrm{i}$ ends at a non-selected candidate parent of $g$. Path $\pi_0$ ends at the parent of $g$ in $T'$ and path $\pi_0$ ends at the last vertex of $\pi_\mathrm{i}$. Let $nca$ denote the NCA of the endpoints of $\pi_0$ and $\pi_0$. The first vertex of $\pi_\mathrm{i}$ is 