Score: $500$ points

问题陈述

存在一个整数序列 $A=(A_1,A_2,\ldots,A_N)$，长度为 $N$，其中所有元素最初都设置为 $0$。同时，存在一个集合 $S$，最初是空的。

按照顺序执行以下 $Q$ 个查询。在处理所有 $Q$ 个查询后，找到序列 $A$ 中每个元素的值。第 $i$ 个查询的格式如下：

• 给定一个整数 $x_i$。如果整数 $x_i$ 包含在 $S$ 中，则从 $S$ 中移除 $x_i$。否则，将 $x_i$ 插入到 $S$ 中。然后，对于每个 $j=1,2,\ldots,N$，如果 $j\in S$，则向 $A_j$ 添加 $|S|$。

这里，$|S|$ 表示集合 $S$ 中元素的数量。例如，如果 $S=\lbrace 3,4,7\rbrace$，那么 $|S|=3$。

以上为大语言模型 kimi 翻译，仅供参考。

Problem Statement

There is an integer sequence $A=(A_1,A_2,\ldots,A_N)$ of length $N$, where all elements are initially set to $0$. Also, there is a set $S$, which is initially empty.

Perform the following $Q$ queries in order. Find the value of each element in the sequence $A$ after processing all $Q$ queries. The $i$-th query is in the following format:

• An integer $x_i$ is given. If the integer $x_i$ is contained in $S$, remove $x_i$ from $S$. Otherwise, insert $x_i$ to $S$. Then, for each $j=1,2,\ldots,N$, add $|S|$ to $A_j$ if $j\in S$.

Here, $|S|$ denotes the number of elements in the set $S$. For example, if $S=\lbrace 3,4,7\rbrace$, then $|S|=3$.

Constraints

• $1\leq N,Q\leq 2\times10^5$
• $1\leq x_i\leq N$
• All given numbers are integers.

Input

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

$N$ $Q$

$x_1$ $x_2$ $\ldots$ $x_Q$

Output

Print the sequence $A$ after processing all queries in the following format:

$A_1$ $A_2$ $\ldots$ $A_N$

Sample Input 1

3 4
1 3 3 2

Sample Output 1

6 2 2

In the first query, $1$ is inserted to $S$, making $S=\lbrace 1\rbrace$. Then, $|S|=1$ is added to $A_1$. The sequence becomes $A=(1,0,0)$.

In the second query, $3$ is inserted to $S$, making $S=\lbrace 1,3\rbrace$. Then, $|S|=2$ is added to $A_1$ and $A_3$. The sequence becomes $A=(3,0,2)$.

In the third query, $3$ is removed from $S$, making $S=\lbrace 1\rbrace$. Then, $|S|=1$ is added to $A_1$. The sequence becomes $A=(4,0,2)$.

In the fourth query, $2$ is inserted to $S$, making $S=\lbrace 1,2\rbrace$. Then, $|S|=2$ is added to $A_1$ and $A_2$. The sequence becomes $A=(6,2,2)$.

Eventually, the sequence becomes $A=(6,2,2)$.

Sample Input 2

4 6
1 2 3 2 4 2

Sample Output 2

15 9 12 7