Common Mistakes

Mistake $1$: Forgetting to process the heavy child first during decomposition. This breaks the chain structure because nodes in the same chain will not get consecutive positions. Mistake $2$: Including the LCA twice when merging the two paths from $u$ and $v$.

The final segment should include the LCA only once. Mistake $3$: Using the wrong segment tree range when querying chains. The order is pos[head[v]] <= pos[v] for all $v$, with the head having the smaller position.