Read problem statements in [Hindi], [Bengali], [Mandarin Chinese], [Russian], and [Vietnamese] as well.

Chef and his friend Chefu decided to go on a trip. The trip takes place over the next $N$ days (numbered 1 through $N$). There are $K$ different places Chef and Chefu could visit (numbered 1 through $K$). They have written a sequence $A_{1}, A_{2}, \ldots, A_{N}$ which denotes the plan of the trip during these $N$ days; however, the plan is not completed yet. For each valid $i$, they want to visit the place $A_{i}$ on the $i$-th day, but if $A_{i} = -1$, then they haven't decided which place to visit on that day.

Chef and his friend do not want to visit the same place two days in a row, but they can visit a place more than once in total. It is not necessary to visit all the places during the trip. Determine whether it is possible to complete the plan in such a way that this condition is satisfied. If it is possible, find one way of completing the plan.

------ Input ------
The first line of the input contains a single integer $T$ denoting the number of test cases. The description of $T$ test cases follows.
The first line of each test case contains two space-separated integers $N$ and $K$.
The second line contains $N$ space-separated integers $A_{1}, A_{2}, \ldots, A_{N}$.

------ Output ------
For each test case, print a line containing the string "YES" if it's possible the complete the plan or "NO" otherwise.

If it's possible to complete the plan, print a second line containing $N$ space-separated integers denoting the sequence $A_{1}, A_{2}, \ldots, A_{N}$ after completing the plan. If there is more than one solution, you may print any one.

------ Constraints ------
$1 ≤ T ≤ 1,000$
$1 ≤ N ≤ 10^{5}$
$2 ≤ K ≤ 10^{5}$
$1 ≤ A_{i} ≤ K$ or $A_{i} = -1$ for each valid $i$
if $A_{i} \neq -1$ and $A_{i+1} \neq -1$, then $A_{i} \neq A_{i+1}$, for each valid $i$
the sum of $N$ over all test cases does not exceed $10^{6}$

------ Subtasks ------
Subtask #1 (30 points):
$N ≤ 1,000$
$K = 2$
the sum of $N$ over all test cases does not exceed $10,000$

Subtask #2 (70 points): original constraints

----- Sample Input 1 ------
5
5 3
-1 -1 -1 -1 -1
4 5
1 2 3 5
3 2
1 -1 2
4 2
1 -1 -1 1
6 4
-1 -1 4 -1 2 -1
----- Sample Output 1 ------
YES
1 2 1 2 1
YES
1 2 3 5
NO
NO
YES
1 2 4 1 2 1

见题面

见题面