Mininum XOR over Tree

You are given a rooted tree with $N$ vertices (numbered $1$ through $N$); vertex $1$ is the root. Each vertex has a weight; let's denote the weight of vertex $i$ by $w_i$. You should answer $Q$ queries. The queries have to be processed online, i.e. to obtain each query, you need the answer to the previous query. In each query, you are given a vertex $v$ and a parameter $k$. For each vertex $u$ i