Stevie : "The best part about Christmas is a Christmas tree. Fantastic to play with". A great goalscorer is one who is remembered even years after he left, just like this guy :

You have been given a tree T consisting of N nodes rooted at node 1 and an array A consisting of M distinct integers.

Now, you need to find the number of distinct triplets $(U,V,K)$ in tree T such that node V lies in the subtree rooted at node U, and the distance between them is exactly $A[K]$. We call the distance between 2 nodes to be the number of edges lying in the shortest path among them.

2 triplets $(U_i,V_i,K_i)$ and $(U_j,V_j,K_j)$ are considered to be distinct, if $U_i \ne U_j$ or $V_i \ne V_j$ or $K_i \ne K_j$.

Can you do it ?

Input Format :

The first line contains 2 space separated integers N and M.

The next line contains M pairwise distinct space separated integers, where the $i^{th}$ integer denotes $A[i]$.

The next line contains $N-1$ space separated integers, where the $i^{th}$ integer denotes the parent of node $i+1$ in tree T.

Output Format:

Print a single integer denoting the required number of valid triplets in tree T

Constraints :

$1 \le N,M \le 200,000$

$0 \le A[i] \le 10^9$ , where $1 \le i \le M$