Definition

It has been handed down that a sequence $v = (a_1,a_2,a_3)$ consisting of 3 elements is a Kadomatsu sequence if $v$ satisfies the following conditions.

1. $a_1,a_2,a_3$ are all distinct
2. Among the 3 elements, $a_2$ is the largest or the smallest

Furthermore, when a sequence $w = (a_1,...,a_n)$ consisting of $n$ elements (where $3\le n$) is such that
any 3 consecutive elements taken from it form a Kadomatsu sequence, $w$ is called a Kadomatsu sequence sequence.

Problem Statement

Determine whether there exists an assignment of $x_1, x_2, \ldots, x_M$ such that the sequence $x_{a_1}, x_{a_2}, \ldots, x_{a_N}$ is a Kadomatsu sequence sequence, and if one exists, output one such assignment.

Input

$N$ $M$
$a_1$ .. $a_N$

$3 \le N \le 10^5$
$1 \le M \le 10^5$
$1 \le a_i \le M$
All values in the input are integers.

Output

If no assignment satisfying the condition exists, output No.

If one exists, output Yes, and then output $x_1, x_2, \ldots, x_M$ separated by newlines or by single-byte spaces.
They must be integers satisfying the constraint $1 \le x_i \le 10^9$.

This problem uses a special judge. There are multiple solutions, and you may output any of them.

Sample

4 3
1 2 3 1

Yes
2 3 1

5 3
1 3 3 3 1

No

6 3
1 2 3 1 2 3

No

9 9
9 8 7 6 5 4 3 2 1

Yes
1 3 2 4 1 3 2 5 4

3 2
2 1 2

No