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.

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.

What is a connected component?

A subgraph of a graph is a graph obtained by choosing some vertices and edges from the original graph.
A graph is said to be connected if and only if one can travel between any two vertices in the graph via edges.
A connected component is a connected subgraph that is not contained in any larger connected subgraph.

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.
$p_1 p_2 \dots p_N$

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.

Sample Input 1

5 3
1 3 4

Sample Output 1

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.

Sample Input 2

5 0

Sample Output 2

1 2 3 4 5

There may be no "レ" mark.

Sample Input 3

10 6
1 2 3 7 8 9

Sample Output 3

4 3 2 1 5 6 10 9 8 7

见题面 Input 部分

见题面 Output 部分