All Tracks Data Structures Trees Binary/ N-ary Trees Problem

Given a Binary tree T consisting of N nodes rooted at node 1 and a number K. each node has a number written on it, where the number written on the \(i^{th}\) node is \(A[i]\).

Now, Monk needs to find the number of unordered triplets \((i,j,k)\), such that node i is an ancestor of node j as well as node k, \(j \ne k\), and \(A[i]+A[j]+A[k] \ge K\).
A node x is considered an ancestor of another node y if x is parent of y or x is an ancestor of parent of y.

Help Monk for the same.

Input Format :

The first line contains 2 space separated integers N and K. The next line contains N 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 represents the parent of node \(i+1\).

Output Format :

Print the required answer on a single line.

Constraints :

\( 1 \le N \le 500 \)

\( 0 \le A[i] ,K \le 10^9 \)

\( 1 \le parent[i] < i\), where \(2 \le i \le N\)

Note :

It is guaranteed that the given input forms a valid binary tree.