Digit Sum

AtCoder

IDdp_s

Time2000ms

Memory256MB

Difficulty—

Find the number of integers between $1$ and $K$ (inclusive) satisfying the following condition, modulo $10^9 + 7$: * The sum of the digits in base ten is a multiple of $D$. ## Constraints * All values in input are integers. * $1 \leq K < 10^{10000}$ * $1 \leq D \leq 100$ ## Input Input is given from Standard Input in the following format: $K$ $D$ [samples]

Samples

Input #1

30
4

Output #1

6

Those six integers are: $4, 8, 13, 17, 22$ and $26$.

Input #2

1000000009
1

Output #2

2

Be sure to print the number modulo $10^9 + 7$.

Input #3

98765432109876543210
58

Output #3

635270834

API Response (JSON)

{
  "problem": {
    "name": "Digit Sum",
    "description": {
      "content": "Find the number of integers between $1$ and $K$ (inclusive) satisfying the following condition, modulo $10^9 + 7$: *   The sum of the digits in base ten is a multiple of $D$.",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "dp_s"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Find the number of integers between $1$ and $K$ (inclusive) satisfying the following condition, modulo $10^9 + 7$:\n\n*   The sum of the digits in base ten is a multiple of $D$.\n\n## Constraints\n\n*   All...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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