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).

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.

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.