Digits Paradise in Hexadecimal

AtCoder

IDabc194_f

Time2000ms

Memory256MB

Difficulty—

In this problem, hexadecimal notations use `0`, ..., `9`, `A`, ..., `F`, representing the values zero through fifteen, respectively. Unless otherwise specified, all notations of numbers are decimal notations. How many integers between $1$ and $N$ (inclusive) have exactly $K$ distinct digits in the hexadecimal notation without leading zeros? Print this count modulo $(10^9 + 7)$. ## Constraints * $1 \le N \lt {16}^{2 \times 10^5}$ * $N$ is given in hexadecimal notation without leading `0`s. * $1 \le K \le 16$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ Here, $N$ is in hexadecimal notation. [samples]

Samples

Input #1

10 1

Output #1

15

The hexadecimal number $N$ is $16$ in decimal.  
In hexadecimal, the integers between $1$ and $16$ are written as follows:

*   $1$ through $15$: are $1$\-digit numbers in hexadecimal, containing one distinct digit.
*   $16$: is $10$ in hexadecimal, containing two distinct digits.

Thus, there are $15$ numbers that contain one distinct digit in hexadecimal.

Input #2

FF 2

Output #2

225

All of the $255$ numbers except the following $30$ numbers contain two distinct digits in hexadecimal: $1, 2, 3, \dots, \mathrm{E}, \mathrm{F}, 11, 22, 33, \dots, \mathrm{EE}, \mathrm{FF}$ in hexadecimal.

Input #3

100 2

Output #3

Input #4

1A8FD02 4

Output #4

Input #5

DEADBEEFDEADBEEEEEEEEF 16

Output #5

153954073

Print the count modulo $(10^9 + 7)$.

API Response (JSON)

{
  "problem": {
    "name": "Digits Paradise in Hexadecimal",
    "description": {
      "content": "In this problem, hexadecimal notations use `0`, ..., `9`, `A`, ..., `F`, representing the values zero through fifteen, respectively.   Unless otherwise specified, all notations of numbers are decimal ",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc194_f"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "In this problem, hexadecimal notations use `0`, ..., `9`, `A`, ..., `F`, representing the values zero through fifteen, respectively.  \nUnless otherwise specified, all notations of numbers are decimal ...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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