Problem Statement

You are given a positive integer N and a sequence of $M positive integers A = (A_{1}, A_{2}, \dots, A_{M})$.
Here, all elements of A are distinct integers between 1 and N, inclusive.
$A permutation P = (P_{1}, P_{2}, \dots, P_{N})$ of $(1, 2, \dots, N)$ is called a good permutation when it satisfies the following condition for all integers i such that $1 \leq i \leq M$:

• No contiguous subsequence of P is a permutation of $(1, 2, \dots, A_{i})$.

Determine whether a good permutation exists, and if it does, find the lexicographically smallest good permutation.
What is lexicographical order?
$A sequence S = (S_1, S_2, \ldots, S_{|S|})$ is said to be lexicographically smaller than $a sequence T = (T_1, T_2, \ldots, T_{|T|})$ if one of the following conditions holds.
Here, |S| and |T| denote the lengths of S and T, respectively.

• $|S| \lt |T|$ and $(S_1, S_2, \ldots, S_{|S|}) = (T_1, T_2, \ldots, T_{|S|})$.

• There exists an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ such that both of the following hold:

• $(S_1, S_2, \ldots, S_{i-1}) = (T_1, T_2, \ldots, T_{i-1})$.

• S_i is smaller than T_i (as a number).

Input

The input is given from Standard Input in the following format:
N M
$A_{1} A_{2} \cdots A_{M}$

Output

If a good permutation does not exist, print -1.
If it exists, print the lexicographically smallest good permutation, separated by spaces.

Constraints

• $1 \leq M \leq N \leq 2 \times 10^{5}$
• $1 \leq A_{i} \leq N$
• All elements of A are distinct.
• All input values are integers.

Sample Input 1

4 1
2

Sample Output 1

1 3 2 4

For example, (4, 2, 1, 3) is not a good permutation because it contains (2, 1) as a contiguous subsequence.
Other non-good permutations are (1, 2, 3, 4) and (3, 4, 2, 1).
Some good permutations are (4, 1, 3, 2) and (2, 3, 4, 1). Among these, the lexicographically smallest one is (1, 3, 2, 4), so print it separated by spaces.

Sample Input 2

5 3
4 3 2

Sample Output 2

1 3 4 5 2

Examples of good permutations include (3, 4, 1, 5, 2), (2, 4, 5, 3, 1), and (4, 1, 5, 2, 3).
Examples of non-good permutations include (1, 2, 5, 3, 4), (2, 3, 4, 1, 5), and (5, 3, 1, 2, 4).

Sample Input 3

92 4
16 7 1 67

Sample Output 3

-1

If a good permutation does not exist, print -1.

Sample Input 4

43 2
43 2

Sample Output 4

-1

见题面 Input 部分

见题面 Output 部分