Keyence Repetition

AtCoder

IDkeyence2021_f

Time6000ms

Memory256MB

Difficulty—

Let $s$ be the concatenation of $N$ copies of `keyence`. Consider deleting zero or more characters from $s$ and concatenating the remaining characters without changing the order to make a new string $s^{\prime}$. There are $2^{7N}$ ways to choose the positions at which we delete the characters. Among them, how many make $s^{\prime}$ equal to $t$? Find the count modulo $998244353$. ## Constraints * $1 \leq N \leq 10^{18}$ * $1 \leq |t| \leq 2.5 \times 10^5$ * $t$ is a string consisting of `c`, `e`, `k`, `n`, and `y`. ## Input Input is given from Standard Input in the following format: $N$ $t$ [samples]

Samples

Input #1

2
key

Output #1

6

*   We have $s=$ `keyencekeyence`.
*   There are six ways to choose the positions at which we delete the characters so that $s^{\prime}=$ `key`.

Input #2

2
ccc

Output #2

0

*   There are zero ways to choose the positions at which we delete the characters so that $s^{\prime}=$ `ccc`.

Input #3

100
keyneeneeeckyycccckkke

Output #3

275429980

*   Be sure to find the count modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Keyence Repetition",
    "description": {
      "content": "Let $s$ be the concatenation of $N$ copies of `keyence`. Consider deleting zero or more characters from $s$ and concatenating the remaining characters without changing the order to make a new string $",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 6000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "keyence2021_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let $s$ be the concatenation of $N$ copies of `keyence`. Consider deleting zero or more characters from $s$ and concatenating the remaining characters without changing the order to make a new string $...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments