ARC Stamp

AtCoder

IDarc131_f

Time3000ms

Memory256MB

Difficulty—

On a string $S$ consisting of `A`, `R`, and `C`, we did the following operation at most $K$ times: choose three consecutive characters and overwrite them with `ARC`. The result is the string $T$. How many strings are there that could be the initial string $S$? Find this count modulo $998244353$. ## Constraints * $3 \leq |T| \leq 5000$ * $0 \leq K \leq 10000$ * $T$ is a string consisting of `A`, `R`, and `C`. ## Input Input is given from Standard Input in the following format: $T$ $K$ [samples]

Samples

Input #1

ARCCARC
1

Output #1

53

Below are some examples of the initial string $S$ from which we can get the string $T$ = `ARCCARC` with at most $1$ operation.

*   $S$ = `ARCCARC`: we can choose to do nothing to get `ARCCARC`.
*   $S$ = `CRACARC`: we can choose the $1$\-st, $2$\-nd, $3$\-rd characters and overwrite them with `ARC` to get `ARCCARC`.
*   $S$ = `ARCCCCC`: we can choose the $5$\-th, $6$\-th, $7$\-th characters and overwrite them with `ARC` to get `ARCCARC`.

There are many other strings that could be $S$, for a total of $53$.

Input #2

ARARCRCA
5

Output #2

2187

If the intial string $S$ is `AAAAAAAA`, one way to get $T$ = `ARARCRCA` with at most $5$ operations is as follows.

*   Step $1$: choose the $3$\-rd, $4$\-th, $5$\-th characters and overwrite them with `ARC` to get the string `AAARCAAA`.
*   Step $2$: choose the $5$\-th, $6$\-th, $7$\-th characters and overwrite them with `ARC` to get the string `AAARARCA`.
*   Step $3$: choose the $1$\-st, $2$\-nd, $3$\-rd characters and overwrite them with `ARC` to get the string `ARCRARCA`.
*   Step $4$: choose the $3$\-rd, $4$\-th, $5$\-th characters and overwrite them with `ARC` to get the string `ARARCRCA`.

There are many other strings that could be $S$, for a total of $2187$.

Input #3

AARCRRARCC
0

Output #3

1

We can get $T$ = `AARCRRARCC` with $0$ operations in only one case in which $S = T$ from the beginning, or $S$ = `AARCRRARCC`.

Input #4

AAAAARRRRRCCCCC
131

Output #4

1

In this case, there is just one string that could be $S$: `AAAAARRRRRCCCCC`.

Input #5

CAARCACRAAARARARCRCRARCARARCRRARC
9

Output #5

797833187

There are $320236026147$ strings that could be $S$, so print this count modulo $998244353$, which is $797833187$.

API Response (JSON)

{
  "problem": {
    "name": "ARC Stamp",
    "description": {
      "content": "On a string $S$ consisting of `A`, `R`, and `C`, we did the following operation at most $K$ times: choose three consecutive characters and overwrite them with `ARC`. The result is the string $T$. How ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 3000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc131_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "On a string $S$ consisting of `A`, `R`, and `C`, we did the following operation at most $K$ times: choose three consecutive characters and overwrite them with `ARC`. The result is the string $T$.\nHow ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments