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.

Input

Input is given from Standard Input in the following format:
N K
$A_1 A_2 \cdots A_K$

Output

Print the answer.

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.

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

见题面 Input 部分

见题面 Output 部分