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 $|S|=3$.

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

```
$N$ $Q$
$x_1$ $x_2$ $\ldots$ $x_Q$
```

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

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

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

6 2 2

In the first query, 1 is inserted to S, making S={1}. 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={1,3}. 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={1}. 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={1,2}. 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).