You are given a tree with N nodes. Each node i has a value $A_{i}$ associated with it. You are asked to perform Q queries on it.
Each query contains an integer i.
In each query, you need to remove the $i^{th}$ edge and find number of connected unordered pair of nodes $u, v$ such that $|A_u - A_v| \leq D$.

Note :
The tree is restored to it's original state after each query.

Input :
The first line of the input contains three single space separated integers $N, D$ and Q.
The next line of the input contains N single space separated integers denoting $A_i$.
Each of the next $N - 1$ lines contains two space separated integers u and v , the nodes that the $i^{th}$ edge connects (Edges are ordered by 1 based index).
Each of the next Q lines of the input contains an integer i corresponding to that query.

Output :
For each query, print the total number of connected unordered pairs $u, v$ such that $| A_u - A_v | \leq D$.

Constraints :

• $2 ≤ N ≤ 10^5$
• $1 ≤ A_i ≤ 10^6$
• $1 ≤ Q ≤ 10^5$
• $0 ≤ D ≤ 20$