Steady Pulse Triplet Count

A wearable heart monitor logs the exact timestamp of every detected heartbeat, in strictly increasing order with no two beats sharing a timestamp. A calibration check considers three logged beats — taken in chronological order — to demonstrate a steady rhythm at a target interval gap if the time from the first beat to the second equals gap, and the time from the second beat to the third also equals gap. Count how many such triples of beats exist in the log (the three beats need not be consecutive entries in the log — only their timestamps must satisfy the two equal gaps).

Input format

The first line contains two integers n and gap — the number of logged beats and the target interval. The second line contains n strictly increasing integers — the beat timestamps.

Output format

Print a single integer: the number of triples (i, j, k) with i < j < k such that timestamp[j] - timestamp[i] = gap and timestamp[k] - timestamp[j] = gap.

Constraints

• 1 <= n <= 10^5
• 1 <= gap <= 10^9
• 1 <= timestamp[i] <= 10^9
• The timestamps are strictly increasing (and therefore all distinct).

5 2
2 4 6 8 10

3

5 1
1 5 6 7 10

1