A triple of points $$$i$$$, $$$j$$$ and $$$k$$$ on a coordinate line is called beautiful if $$$i < j < k$$$ and $$$k - i \le d$$$.
You are given a set of points on a coordinate line, initially empty. You have to process queries of three types:
The first line contains two integers $$$q$$$ and $$$d$$$ ($$$1 \le q, d \le 2 \cdot 10^5$$$) — the number of queries and the parameter for defining if a triple is beautiful, respectively.
The second line contains $$$q$$$ integers $$$a_1, a_2, \dots, a_q$$$ ($$$1 \le a_i \le 2 \cdot 10^5$$$) denoting the queries. The integer $$$a_i$$$ denotes the $$$i$$$-th query in the following way:
For each query, print one integer — the number of beautiful triples after processing the respective query.
7 5 8 5 3 2 1 5 6
0 0 1 2 5 1 5
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