#(subset sum = K) with Add and Erase

AtCoder

IDabc321_f

Time2000ms

Memory256MB

Difficulty—

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. ## Constraints * 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. ## Input 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}$ [samples]

Samples

Input #1

15 10
+ 5
+ 2
+ 3
- 2
+ 5
+ 10
- 3
+ 1
+ 3
+ 3
- 5
+ 1
+ 7
+ 4
- 3

Output #1

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)

API Response (JSON)

{
  "problem": {
    "name": "#(subset sum = K) with Add and Erase",
    "description": {
      "content": "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",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc321_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a box, which is initially empty.  \nLet us perform a total of $Q$ operations of the following two types in the order they are given in the input.\n\n\\+ $x$\n\nType $1$: Put into the box a ball with...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments