Points

6000ms

524288K

Description:

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:

add a point;
remove a point;
calculate the number of beautiful triples consisting of points belonging to the set.

Input:

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:

if the point $$$a_i$$$ belongs to the set, remove it; otherwise, add it;
after adding or removing the point, print the number of beautiful triples.

Output:

For each query, print one integer — the number of beautiful triples after processing the respective query.

Sample Input:

7 5
8 5 3 2 1 5 6

Sample Output:

Informação

Provedor Codeforces

Código CF1701F