Core Idea - Handling Invalid Queries

If $k$ is larger than the depth of $v$, there is no $k$-th ancestor. You will jump past the root. Handle this by checking if $v$ becomes $-1$ or null during the jumps.

If so, return $-1$. Alternatively, compute depth and check k > depth[v] before jumping. Either approach works. The jumping method is simpler because you do not need to precompute depths separately. If up[root][0] = root, you will stay at root forever, so also check if you have jumped more times than needed.