Space Improvement

Binary lifting uses $O(n \log n)$ space for the jump table. For large $n$, this might exceed memory limits. You need alternatives that trade space for time. One improvement: compute jumps on-the-fly using recursion with memoization. This trades time for space. You compute jumps as needed rather than precomputing everything.

Cache results to avoid recomputation. Another approach: use square root decomposition. Store jumps for $\sqrt{n}$ intervals and combine. This reduces space to $O(n\sqrt{n})$ with slightly worse query time of $O(\sqrt{n})$ instead of $O(\log n)$. Pick based on constraints.