You are given a tree with $N$ nodes and $N-1$ edges and an integer $K$. Each node has a label denoted by an integer, $A_i$. Your task is to find the length of the longest path such that label of all the nodes in the path are divisible by $K$.

Length of a path is the number of edges in that path.

Input Format:

First line contains two space separated integers, $N$ and $K$. Next line contains $N$ space separated integers, $i^{th}$ integer denotes the label of $i^{th}$ node, $A_i$. Next $N-1$ lines contains two space separated integers each, $U$ and $V$ denoting that there is an edge between node $U$ and node $V$.

Output Format:

Print a single integer denoting the length of the longest path such that label of all the nodes in the path are divisible by $K$.

Constraints:

$1 \le N \le 10^5$

$1 \le K \le 10^5$

$1 \le A_i \le 10^5$

$1 \le U, V \le N$