Snuke Numbers

AtCoder

IDarc099_b

Time2000ms

Memory256MB

Difficulty—

Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(123) = 1 + 2 + 3 = 6$. We will call an integer $n$ a **Snuke number** when, for all positive integers $m$ such that $m > n$, $\frac{n}{S(n)} \leq \frac{m}{S(m)}$ holds. Given an integer $K$, list the $K$ smallest Snuke numbers. ## Constraints * $1 \leq K$ * The $K$\-th smallest Snuke number is not greater than $10^{15}$. ## Input Input is given from Standard Input in the following format: $K$ [samples]

Samples

Input #1

Output #1

API Response (JSON)

{
  "problem": {
    "name": "Snuke Numbers",
    "description": {
      "content": "Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(123) = 1 + 2 + 3 = 6$. We will call an integer $n$ a **Snuke number** when, for all positive integers $m$ such t",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "arc099_b"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Let $S(n)$ denote the sum of the digits in the decimal notation of $n$. For example, $S(123) = 1 + 2 + 3 = 6$.\nWe will call an integer $n$ a **Snuke number** when, for all positive integers $m$ such t...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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