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 \( 1 \le i \le M \)