Buy an Integer

AtCoder

IDabc146_c

Time2000ms

Memory256MB

Difficulty—

Takahashi has come to an integer shop to buy an integer. The shop sells the integers from $1$ through $10^9$. The integer $N$ is sold for $A \times N + B \times d(N)$ yen (the currency of Japan), where $d(N)$ is the number of digits in the decimal notation of $N$. Find the largest integer that Takahashi can buy when he has $X$ yen. If no integer can be bought, print $0$. ## Constraints * All values in input are integers. * $1 \leq A \leq 10^9$ * $1 \leq B \leq 10^9$ * $1 \leq X \leq 10^{18}$ ## Input Input is given from Standard Input in the following format: $A$ $B$ $X$ [samples]

Samples

Input #1

10 7 100

Output #1

9

The integer $9$ is sold for $10 \times 9 + 7 \times 1 = 97$ yen, and this is the greatest integer that can be bought. Some of the other integers are sold for the following prices:

*   $10: 10 \times 10 + 7 \times 2 = 114$ yen
*   $100: 10 \times 100 + 7 \times 3 = 1021$ yen
*   $12345: 10 \times 12345 + 7 \times 5 = 123485$ yen

Input #2

2 1 100000000000

Output #2

1000000000

He can buy the largest integer that is sold. Note that input may not fit into a $32$\-bit integer type.

Input #3

1000000000 1000000000 100

Output #3

Input #4

1234 56789 314159265

Output #4

API Response (JSON)

{
  "problem": {
    "name": "Buy an Integer",
    "description": {
      "content": "Takahashi has come to an integer shop to buy an integer. The shop sells the integers from $1$ through $10^9$. The integer $N$ is sold for $A \\times N + B \\times d(N)$ yen (the currency of Japan), wher",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc146_c"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "Takahashi has come to an integer shop to buy an integer.\nThe shop sells the integers from $1$ through $10^9$. The integer $N$ is sold for $A \\times N + B \\times d(N)$ yen (the currency of Japan), wher...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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