Variety of Digits

AtCoder

IDabc235_f

Time2000ms

Memory256MB

Difficulty—

Given are $M$ digits $C_i$. Find the sum, modulo $998244353$, of all integers between $1$ and $N$ (inclusive) that contain all of $C_1, \ldots, C_M$ when written in base $10$ without unnecessary leading zeros. ## Constraints * $1 \leq N < 10^{10^4}$ * $1 \leq M \leq 10$ * $0 \leq C_1 < \ldots < C_M \leq 9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $M$ $C_1$ $\ldots$ $C_M$ [samples]

Samples

Input #1

104
2
0 1

Output #1

520

Between $1$ and $104$, there are six integers that contain both `0` and `1` when written in base $10$: $10,100,101,102,103,104$.  
The sum of them is $520$.

Input #2

999
4
1 2 3 4

Output #2

0

Between $1$ and $999$, no integer contains all of `1`, `2`, `3`, `4`.

Input #3

1234567890123456789012345678901234567890123456789012345678901234567890123456789012345678901234567890
5
0 2 4 6 8

Output #3

397365274

Be sure to find the sum modulo $998244353$.

API Response (JSON)

{
  "problem": {
    "name": "Variety of Digits",
    "description": {
      "content": "Given are $M$ digits $C_i$. Find the sum, modulo $998244353$, of all integers between $1$ and $N$ (inclusive) that contain all of $C_1, \\ldots, C_M$ when written in base $10$ without unnecessary leadi",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc235_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Given are $M$ digits $C_i$.\nFind the sum, modulo $998244353$, of all integers between $1$ and $N$ (inclusive) that contain all of $C_1, \\ldots, C_M$ when written in base $10$ without unnecessary leadi...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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