We have a box, which is initially empty.  
Let us perform a total of $Q$ operations of the following two types in the order they are given in the input.

```
+ $x$
```

Type $1$: Put into the box a ball with the integer $x$ written on it.

```
- $x$
```

Type $2$: Remove from the box a ball with the integer $x$ written on it.  
It is guaranteed that the box contains a ball with the integer $x$ written on it before the operation.

  

For the box after each operation, solve the following problem.

> Find the number, modulo $998244353$, to pick up some number of balls from the box so that the integers written on them sum to $K$.  
> All balls in the box are distinguishable.

The input is given from Standard Input in the following format, where $\mathrm{Query}_i$ represents the $i$-th operation:

```
$Q$ $K$
$\rm{Query}$$_{1}$
$\rm{Query}$$_{2}$
$\vdots$
$\rm{Query}$$_{Q}$
```

Print $Q$ lines.  
The $i$-th line should contain the answer when the first $i$ operations have been done.

-   All input values are integers.
-   $1 \le Q \le 5000$
-   $1 \le K \le 5000$
-   For each type-$1$ operation, $1 \le x \le 5000$.
-   All the operations satisfy the condition in the problem statement.

0
0
1
0
1
2
2
2
2
2
1
3
5
8
5

This input contains 15 operations.
After the last operation, the box contains the balls (5,10,1,3,1,7,4).
There are five ways to pick up balls for a sum of 10:

• 5+1+3+1 (the 1-st, 3-rd, 4-th, 5-th balls)
• 5+1+4 (the 1-st, 3-rd, 7-th balls)
• 5+1+4 (the 1-st, 5-th, 7-th balls)
• 10 (the 2-nd ball)
• 3+7 (the 4-th, 6-th balls)