222

AtCoder

IDabc222_g

Time2000ms

Memory256MB

Difficulty—

We have a sequence $2,22,222,2222,\ldots$, where the $i$\-th term is an $i$\-digit integer whose digits are all $2$. Where does a multiple of $K$ appear in this sequence for the first time? If the first multiple of $K$ is the $x$\-th term of the sequence, print $x$; if there is no multiple of $K$, print `-1`. Given $T$ cases, solve each of them. ## Constraints * $1 \leq T \leq 200$ * $1 \leq K \leq 10^8$ * All values in input are integers. ## Input Input is given from Standard Input in the following format: $T$ $\text{case}_1$ $\text{case}_2$ $\vdots$ $\text{case}_T$ Each case is in the following format: $K$ [samples]

Samples

Input #1

Output #1

1
6
-1
999982

We have four cases.

*   $2$ is a multiple of $1$.
*   None of $2,22,222,2222,22222$ is a multiple of $7$, but $222222$ is.
*   None of $2,22,\ldots$ is a multiple of $10$.

API Response (JSON)

{
  "problem": {
    "name": "222",
    "description": {
      "content": "We have a sequence $2,22,222,2222,\\ldots$, where the $i$\\-th term is an $i$\\-digit integer whose digits are all $2$. Where does a multiple of $K$ appear in this sequence for the first time? If the fir",
      "description_type": "Markdown"
    },
    "platform": "AtCoder",
    "limit": {
      "time_limit": 2000,
      "memory_limit": 262144
    },
    "difficulty": "None",
    "is_remote": true,
    "is_sync": true,
    "sync_url": null,
    "sign": "abc222_g"
  },
  "statements": [
    {
      "statement_type": "Markdown",
      "content": "We have a sequence $2,22,222,2222,\\ldots$, where the $i$\\-th term is an $i$\\-digit integer whose digits are all $2$.\nWhere does a multiple of $K$ appear in this sequence for the first time? If the fir...",
      "is_translate": false,
      "language": "English"
    }
  ]
}

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