Tree difference

You are given a tree with $N$ nodes (numbered $1$ through $N$). For each valid $i$, node $i$ has a value $A_i$. You should answer $Q$ queries. In each query: - You are given two nodes $a$ and $b$. - Let $S$ denote the set of all nodes on the simple path between the nodes $a$ and $b$ (including these nodes). - Find the minimum value of $|A_x-A_y|$ over all pairs $x, y \in S$ such that $x \neq