Priority Queue

AtCoder

IDarc127_e

Time2000ms

Memory256MB

Difficulty—

Given is a sequence of $A+B$ integers $(X_1,X_2,\cdots,X_{A+B})$, which contains exactly $A$ ones and exactly $B$ twos. Snuke has a set $s$, which is initially empty. He is going to do $A+B$ operations. The $i$\-th operation is as follows. * If $X_i=1$: Choose an integer $v$ such that $1 \leq v \leq A$ and add it to $s$. Here, $v$ must not be an integer that was chosen in a previous operation. * If $X_i=2$: Delete from $s$ the element with the largest value. The input guarantees that $s$ is not empty just before this operation. How many sets are there that can be the final state of $s$? Find the count modulo $998244353$. ## Constraints * $1 \leq A \leq 5000$ * $0 \leq B \leq A-1$ * $1 \leq X_i \leq 2$ * $X_i=1$ for exactly $A$ indices $i$. * $X_i=2$ for exactly $B$ indices $i$. * $s$ will not be empty just before an operation with $X_i=2$. * All values in input are integers. ## Input Input is given from Standard Input in the following format: $A$ $B$ $X_1$ $X_2$ $\cdots$ $X_{A+B}$ [samples]

Samples

Input #1

3 1
1 1 2 1

Output #1

2

There are two possible final states of $s$: $s={1,2},{1,3}$.
For example, the following sequence of operations results in $s={1,3}$.

*   $i=1$: Add $2$ to $s$.
*   $i=2$: Add $1$ to $s$.
*   $i=3$: Delete $2$ from $s$.
*   $i=4$: Add $3$ to $s$.

Input #2

20 6
1 1 1 1 1 2 1 1 1 2 1 2 1 2 1 2 1 1 1 1 2 1 1 1 1 1

Output #2

API Response (JSON)

{
  "problem": {
    "name": "Priority Queue",
    "description": {
      "content": "Given is a sequence of $A+B$ integers $(X_1,X_2,\\cdots,X_{A+B})$, which contains exactly $A$ ones and exactly $B$ twos. Snuke has a set $s$, which is initially empty. He is going to do $A+B$ operation",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc127_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given is a sequence of $A+B$ integers $(X_1,X_2,\\cdots,X_{A+B})$, which contains exactly $A$ ones and exactly $B$ twos.\nSnuke has a set $s$, which is initially empty. He is going to do $A+B$ operation...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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