201252: [AtCoder]ARC125 C - LIS to Original Sequence

Problem Statement

Given are an integer $N$ and a monotonically increasing sequence of $K$ integers $A=(A_1,A_2,\cdots,A_K)$. Find the lexicographically smallest permutation $P$ of $(1,2,\cdots,N)$ that satisfies the following condition.

• $A$ is a longest increasing subsequence of $P$ (a monotonically increasing subsequence of $P$ with the maximum possible length). It is fine if $P$ has multiple longest increasing subsequences, one of which is $A$.

From the Constraints of this problem, we can prove that there always exists a $P$ that satisfies the condition.

Constraints

• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq A_1 < A_2 < \cdots < A_K \leq N$
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$
$A_1$ $A_2$ $\cdots$ $A_K$

Output

Print the answer.

Sample Input 1

3 2
2 3

Sample Output 1

2 1 3

$A$ is a longest increasing subsequence of $P$ when $P=(2,1,3),(2,3,1)$. The answer is the lexicographically smallest of the two, or $(2,1,3)$.

Sample Input 2

5 1
4

Sample Output 2

5 4 3 2 1