You are an expert competitive programmer. You will be given a problem statement, test case constraints and example test inputs and outputs. Please reason step by step about the solution (that must respect memory and time limits), then provide a complete implementation in c++17.

Your solution must read input from standard input (cin), write output to standard output (cout).
Do not include any debug prints or additional output.

Put your final solution within a single code block:
```cpp
<your code here>
```

Execution time limit: 1.0 seconds
Memory limit: 256.0 MB

# Problem
Initially there was an array $$$a$$$ consisting of $$$n$$$ integers. Positions in it are numbered from $$$1$$$ to $$$n$$$.

Exactly $$$q$$$ queries were performed on the array. During the $$$i$$$-th query some segment $$$(l_i, r_i)$$$ $$$(1 \le l_i \le r_i \le n)$$$ was selected and values of elements on positions from $$$l_i$$$ to $$$r_i$$$ inclusive got changed to $$$i$$$. The order of the queries couldn't be changed and all $$$q$$$ queries were applied. It is also known that every position from $$$1$$$ to $$$n$$$ got covered by at least one segment.

We could have offered you the problem about checking if some given array (consisting of $$$n$$$ integers with values from $$$1$$$ to $$$q$$$) can be obtained by the aforementioned queries. However, we decided that it will come too easy for you.

So the enhancement we introduced to it is the following. Some set of positions (possibly empty) in this array is selected and values of elements on these positions are set to $$$0$$$.

Your task is to check if this array can be obtained by the aforementioned queries. Also if it can be obtained then restore this array.

If there are multiple possible arrays then print any of them.

## Input Format
The first line contains two integers $$$n$$$ and $$$q$$$ ($$$1 \le n, q \le 2 \cdot 10^5$$$) — the number of elements of the array and the number of queries perfomed on it.

The second line contains $$$n$$$ integer numbers $$$a_1, a_2, \dots, a_n$$$ ($$$0 \le a_i \le q$$$) — the resulting array. If element at some position $$$j$$$ is equal to $$$0$$$ then the value of element at this position can be any integer from $$$1$$$ to $$$q$$$.

## Output Format
Print "YES" if the array $$$a$$$ can be obtained by performing $$$q$$$ queries. Segments $$$(l_i, r_i)$$$ $$$(1 \le l_i \le r_i \le n)$$$ are chosen separately for each query. Every position from $$$1$$$ to $$$n$$$ should be covered by at least one segment.

Otherwise print "NO".

If some array can be obtained then print $$$n$$$ integers on the second line — the $$$i$$$-th number should be equal to the $$$i$$$-th element of the resulting array and should have value from $$$1$$$ to $$$q$$$. This array should be obtainable by performing exactly $$$q$$$ queries.

If there are multiple possible arrays then print any of them.

## Examples
```input
4 3
1 0 2 3
```
```output
YES
1 2 2 3
```
-----
```input
3 10
10 10 10
```
```output
YES
10 10 10
```
-----
```input
5 6
6 5 6 2 2
```
```output
NO
```
-----
```input
3 5
0 0 0
```
```output
YES
5 4 2
```

## Note
In the first example you can also replace $$$0$$$ with $$$1$$$ but not with $$$3$$$.

In the second example it doesn't really matter what segments to choose until query $$$10$$$ when the segment is $$$(1, 3)$$$.

The third example showcases the fact that the order of queries can't be changed, you can't firstly set $$$(1, 3)$$$ to $$$6$$$ and after that change $$$(2, 2)$$$ to $$$5$$$. The segment of $$$5$$$ should be applied before segment of $$$6$$$.

There is a lot of correct resulting arrays for the fourth example.

Now solve the problem and return the code.