[Solution] Points Codeforces Solution | Codeforces 2022

F. Points

time limit per test

6.5 seconds

memory limit per test

512 megabytes

input

standard input

output

standard output

A triple of points i$i$, j$j$ and k$k$ on a coordinate line is called beautiful if i<j<k$i<j<k$ and k−i≤d$k-i\le d$.

You are given a set of points on a coordinate line, initially empty. You have to process queries of three types:

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• 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$q$ and d$d$ (1≤q,d≤2⋅105$1\le q,d\le 2\cdot {10}^5$) — the number of queries and the parameter for defining if a triple is beautiful, respectively.

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The second line contains q$q$ integers a1,a2,…,aq$a_1,a_2,\dots ,a_q$ (1≤ai≤2⋅105$1\le a_i\le 2\cdot {10}^5$) denoting the queries. The integer ai$a_i$ denotes the i$i$-th query in the following way:

• if the point ai$a_i$ 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.