Score : $200$ points

Problem Statement

Studying Kanbun

, Takahashi is having trouble figuring out the order to read words. Help him out!

There are $N$ integers from $1$ through $N$ arranged in a line in ascending order.
Between them are $M$ "レ" marks. The $i$-th "レ" mark is between the integer $a_i$ and integer $(a_i + 1)$.

You read each of the $N$ integers once by the following procedure.

• Consider an undirected graph $G$ with $N$ vertices numbered $1$ through $N$ and $M$ edges. The $i$-th edge connects vertex $a_i$ and vertex $(a_i+1)$.
• Repeat the following operation until there is no unread integer:- let $x$ be the minimum unread integer. Choose the connected component $C$ containing vertex $x$, and read all the numbers of the vertices contained in $C$ in descending order.
• let $x$ be the minimum unread integer. Choose the connected component $C$ containing vertex $x$, and read all the numbers of the vertices contained in $C$ in descending order.

For example, suppose that integers and "レ" marks are arranged in the following order:

(In this case, $N = 5, M = 3$, and $a = (1, 3, 4)$.) Then, the order to read the integers is determined to be $2, 1, 5, 4$, and $3$, as follows:

• At first, the minimum unread integer is $1$, and the connected component of $G$ containing vertex $1$ has vertices $\lbrace 1, 2 \rbrace$, so $2$ and $1$ are read in this order.
• Then, the minimum unread integer is $3$, and the connected component of $G$ containing vertex $3$ has vertices $\lbrace 3, 4, 5 \rbrace$, so $5$, $4$, and $3$ are read in this order.
• Now that all integers are read, terminate the procedure.

Given $N, M$, and $(a_1, a_2, \dots, a_M)$, print the order to read the $N$ integers.

Constraints

• $1 \leq N \leq 100$
• $0 \leq M \leq N - 1$
• $1 \leq a_1 \lt a_2 \lt \dots \lt a_M \leq N-1$
• All values in the input are integers.

Input

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

$N$ $M$

$a_1$ $a_2$ $\dots$ $a_M$

Output

Print the answer in the following format, where $p_i$ is the $i$-th integers to read.

$p_1$ $p_2$ $\dots$ $p_N$

5 3
1 3 4

2 1 5 4 3

As described in the Problem Statement, if integers and "レ" marks are arranged in the following order:

then the integers are read in the following order: $2, 1, 5, 4$, and $3$.

5 0

1 2 3 4 5

There may be no "レ" mark.

10 6
1 2 3 7 8 9

4 3 2 1 5 6 10 9 8 7