LuoTianyi and the Show
Description
There are $n$ people taking part in a show about VOCALOID. They will sit in the row of seats, numbered $1$ to $m$ from left to right.
The $n$ people come and sit in order. Each person occupies a seat in one of three ways:
- Sit in the seat next to the left of the leftmost person who is already sitting, or if seat $1$ is taken, then leave the show. If there is no one currently sitting, sit in seat $m$.
- Sit in the seat next to the right of the rightmost person who is already sitting, or if seat $m$ is taken, then leave the show. If there is no one currently sitting, sit in seat $1$.
- Sit in the seat numbered $x_i$. If this seat is taken, then leave the show.
Now you want to know what is the maximum number of people that can take a seat, if you can let people into the show in any order?
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 10^5$) — the number of people and the number of seats.
The second line of each test case contains $n$ integers $x_1, x_2, \ldots, x_n$ ($-2 \le x_i \le m$, $x_i \ne 0$), the $i$-th of which describes the way in which the $i$-th person occupies a seat:
- If $x_i=-1$, then $i$-th person takes the seat in the first way.
- If $x_i=-2$, then $i$-th person takes the seat in the second way.
- If $x_i > 0$, then the $i$-th person takes a seat in the third way, i.e. he wants to sit in the seat with the number $x_i$ or leave the show if it is occupied..
It is guaranteed that sum of $n$ and the sum of $m$ over all test cases don't exceed $10^5$.
For each test case output a single integer — the maximum number of people who can occupy a seat.
Input
Each test consists of multiple test cases. The first line contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases. The description of test cases follows.
The first line of each test case contains two integers $n$ and $m$ ($1 \le n, m \le 10^5$) — the number of people and the number of seats.
The second line of each test case contains $n$ integers $x_1, x_2, \ldots, x_n$ ($-2 \le x_i \le m$, $x_i \ne 0$), the $i$-th of which describes the way in which the $i$-th person occupies a seat:
- If $x_i=-1$, then $i$-th person takes the seat in the first way.
- If $x_i=-2$, then $i$-th person takes the seat in the second way.
- If $x_i > 0$, then the $i$-th person takes a seat in the third way, i.e. he wants to sit in the seat with the number $x_i$ or leave the show if it is occupied..
It is guaranteed that sum of $n$ and the sum of $m$ over all test cases don't exceed $10^5$.
Output
For each test case output a single integer — the maximum number of people who can occupy a seat.
10
3 10
5 5 5
4 6
1 -2 -2 1
5 7
-1 -1 4 -2 -2
6 7
5 -2 -2 -2 -2 -2
6 6
-1 1 4 5 -1 4
6 8
-1 -1 -1 3 -1 -2
6 7
5 -1 -2 -2 -2 -2
3 1
-2 -2 1
2 5
5 -2
1 2
-1
1
3
5
6
5
5
5
1
2
1
Note
In the first test case, all the people want to occupy the $5$ seat, so only $1$ people can occupy the seat.
In the second test case, we can let people in order $1, 2, 3, 4$, then all but the last person can take a seat.
In the third test case, we can let people into the show in that order:
Let the third person in:
| – | – | – | 3 | – | – | – |
Let the fourth person in:
| – | – | – | 3 | 4 | – | – |
Let the fifth person in:
| – | – | – | 3 | 4 | 5 | – |
Let the first person in:
| – | – | 1 | 3 | 4 | 5 | – |
Let the second person in:
| – | 2 | 1 | 3 | 4 | 5 | – |
Thus, all $5$ people took seats.
In the fifth test case, we can let people into the show in this order:
Let the fourth person in:
| – | – | – | – | 4 | – |
Let the third person in:
| – | – | – | 3 | 4 | – |
Let the sixth person in, he'll leave the show because he takes the third seat the third way and has to sit in the $4$ seat, but it's already taken:
| – | – | – | 3 | 4 | – |
Let the fifth person in:
| – | – | 5 | 3 | 4 | – |
Let the first person in:
| – | 1 | 5 | 3 | 4 | – |
Let the second person in:
| 2 | 1 | 5 | 3 | 4 | – |
Thus, $5$ of people took seats.
In the seventh test case, we can let people into the show in this order:
Let the third person in:
| 3 | – | – | – | – | – | – |
Let the fourth person in:
| 3 | 4 | – | – | – | – | – |
Let the fifth person in:
| 3 | 4 | 5 | – | – | – | – |
Let the sixth person in:
| 3 | 4 | 5 | 6 | – | – | – |
Let the first person in:
| 3 | 4 | 5 | 6 | 1 | – | – |
Let the second person in, he will leave the show because he occupies the first way, but the $1$ seat is taken:
| 3 | 4 | 5 | 6 | 1 | – | – |
Thus, $5$ people took seats.