Tree and Divisors

You are given a tree with $N$ vertices, rooted at vertex $1$. The $i$-th vertex of this tree has the integer $A_i$ written on it. For each vertex $u$ ($1 \leq u \leq N$), find the number of divisors of the product of all $A_v$ such that $v$ lies in the subtree of $u$. Formally, for each $u$: - Let $S_u$ denote the set of vertices that lie in the subtree of $u$ (including $u$). - Define $X_u = \p