Monk and Tree Counting
Tag(s):

## Data Structures, Easy-Medium

Problem
Editorial
Analytics

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.

SAMPLE INPUT
5 6
1 2 3 4 5
1 2 2 1
SAMPLE OUTPUT
7
Explanation

Image of the tree is given below

The triplets forming part of the answer are :

1. $(1,2,3)$

2. $(1,2,4)$

3. $(1,2,5)$

4. $(1,3,4)$

5. $(1,3,5)$.

6. $(1,4,5)$.

7. $(2,3,4)$

Time Limit: 1.0 sec(s) for each input file.
Memory Limit: 256 MB
Source Limit: 1024 KB
Marking Scheme: Marks are awarded when all the testcases pass.
Allowed Languages: C, C++, C++14, Clojure, C#, D, Erlang, F#, Go, Groovy, Haskell, Java, Java 8, JavaScript(Rhino), JavaScript(Node.js), Julia, Kotlin, Lisp, Lisp (SBCL), Lua, Objective-C, OCaml, Octave, Pascal, Perl, PHP, Python, Python 3, R(RScript), Racket, Ruby, Rust, Scala, Swift, Visual Basic

## CODE EDITOR

Initializing Code Editor...

## This Problem was Asked in

Challenge Name

CodeMonk (Trees)

OTHER PROBLEMS OF THIS CHALLENGE
• Data Structures > Trees
• Data Structures > Trees
• Data Structures > Trees
• Data Structures > Trees