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  1. Practice
  2. Algorithms
  3. Implementation
  4. Beautiful Triplets

Beautiful Triplets

Given a sequence of integers , a triplet is beautiful if:

Given an increasing sequenc of integers and the value of , count the number of beautiful triplets in the sequence.

For example, the sequence and . There are three beautiful triplets, by index: . To test the first triplet, and .

Function Description

Complete the beautifulTriplets function in the editor below. It must return an integer that represents the number of beautiful triplets in the sequence.

beautifulTriplets has the following parameters:

  • d: an integer
  • arr: an array of integers, sorted ascending

Input Format

The first line contains space-separated integers and , the length of the sequence and the beautiful difference.
The second line contains space-separated integers .

Constraints

Output Format

Print a single line denoting the number of beautiful triplets in the sequence.

Sample Input

7 3
1 2 4 5 7 8 10

Sample Output

3

Explanation

The input sequence is , and our beautiful difference . There are many possible triplets , but our only beautiful triplets are , and by value not index. Please see the equations below:




Recall that a beautiful triplet satisfies the following equivalence relation: where .