Tree and Brilliant Array

You are given a positive integer $K$ and a tree with $N$ vertices, rooted at vertex $1$. For all integer $i$ ($2 \leq i \leq N$), $P_i$ is a parent of vertex $i$. Let's call an array $A$ consisting of $N$ positive integers **brilliant** if the following constraints are met - $A_{P_i}\bmod A_i = 0$, for all integer $i$ ($2 \leq i \leq N$). - $\prod_{i=1}^N A_i \leq K$. Compute remainder modulo $