Score : $525$ points

问题陈述

给定一个整数 $K$。对于一个最初为空的集合 $S$，按顺序处理 $Q$ 个查询，包括以下两种类型：

• 1 x：给定一个整数 $x$。如果 $x$ 在 $S$ 中，则从 $S$ 中移除 $x$。否则，将 $x$ 添加到 $S$。
• 2 x：给定一个在 $S$ 中的整数 $x$。考虑一个图，其中顶点是 $S$ 中的数字，并且只有当两个数字之间的绝对差值最多为 $K$ 时，这两个数字之间才有边。打印包含 $x$ 的连通分量中的顶点数。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

You are given an integer $K$. For a set $S$ that is initially empty, process $Q$ queries of the following two types in order:

• 1 x: An integer $x$ is given. If $x$ is in $S$, remove $x$ from $S$. Otherwise, add $x$ to $S$.
• 2 x: An integer $x$ that is in $S$ is given. Consider a graph where the vertices are the numbers in $S$, and there is an edge between two numbers if and only if the absolute difference between them is at most $K$. Print the count of vertices in the connected component that contains $x$.

Constraints

• $1 \leq Q \leq 2\times 10^5$
• $0 \leq K \leq 10^{18}$
• For each query, $1 \leq x \leq 10^{18}$.
• For each query of the second type, the given $x$ is in $S$ at that point.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

$Q$ $K$

$\mathrm{query}_1$

$\vdots$

$\mathrm{query}_Q$

Each query is given in the following format:

$1$ $x$

$2$ $x$

Output

Process the queries.

Sample Input 1

7 5
1 3
1 10
2 3
1 7
2 3
1 10
2 3

Sample Output 1

1
3
2

The query processing proceeds as follows:

• In the first query, $3$ is added to $S$, resulting in $S=\{3\}$.
• In the second query, $10$ is added to $S$, resulting in $S=\{3,10\}$.
• In the third query, consider a graph with vertices $3$ and $10$ and no edges. The connected component containing $3$ has a size of $1$, so print $1$.
• In the fourth query, $7$ is added to $S$, resulting in $S=\{3,7,10\}$.
• In the fifth query, consider a graph with vertices $3$, $7$, and $10$, with edges between $3$ and $7$, and $7$ and $10$. The connected component containing $3$ has a size of $3$, so print $3$.
• In the sixth query, $10$ is removed from $S$, resulting in $S=\{3,7\}$.
• In the seventh query, consider a graph with vertices $3$ and $7$, with an edge between them. The connected component containing $3$ has a size of $2$, so print $2$.

Sample Input 2

11 1000000000000000000
1 1
1 100
1 10000
1 1000000
1 100000000
1 10000000000
1 1000000000000
1 100000000000000
1 10000000000000000
1 1000000000000000000
2 1

Sample Output 2

10

Sample Input 3

8 0
1 1
1 2
2 1
1 1
1 2
1 1
1 2
2 1

Sample Output 3

1
1