Digit Products

AtCoder

IDabc208_e

Time2000ms

Memory256MB

Difficulty—

For how many positive integers at most $N$ is the product of the digits at most $K$? ## Constraints * $1 \leq N \leq 10^{18}$ * $1 \leq K \leq 10^9$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $N$ $K$ [samples]

Samples

Input #1

13 2

Output #1

5

Out of the positive integers at most $13$, there are five such that the product of the digits is at most $2$: $1$, $2$, $10$, $11$, and $12$.

Input #2

100 80

Output #2

99

Out of the positive integers at most $100$, all but $99$ satisfy the condition.

Input #3

1000000000000000000 1000000000

Output #3

841103275147365677

Note that the answer may not fit into a $32$\-bit integer.

API Response (JSON)

{
  "problem": {
    "name": "Digit Products",
    "description": {
      "content": "For how many positive integers at most $N$ is the product of the digits at most $K$?",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc208_e"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "For how many positive integers at most $N$ is the product of the digits at most $K$?\n\n## Constraints\n\n*   $1 \\leq N \\leq 10^{18}$\n*   $1 \\leq K \\leq 10^9$\n*   All values in input are integers.\n\n## Inp...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

Full JSON Raw Segments