Arithmetic Jumping

You are given a [tree](https://en.wikipedia.org/wiki/Tree_(data_structure)) with $N$ vertices. We call a sequence of vertices $[A_1, A_2, \ldots, A_K]$ *cool* if $dis(A_i, A_{(i+1)}) = i$ for $1 \leq i \lt K$. Here, $dis(u, v)$ denotes the length of the shortest path between vertices $u$ and $v$. Note that, the sequence $A$ may contain **duplicate** vertices as well. You need to answer $M$ qu