Score : $600$ points

问题描述

我们有一个序列 $2,22,222,2222,\ldots$，其中第 $i$ 项是一个由全部为 $2$ 的数字组成的 $i$ 位整数。

在这个序列中，首次出现 $K$ 的倍数是在哪个位置？如果第一个 $K$ 的倍数是序列中的第 $x$ 项，则输出 $x$；如果没有 $K$ 的倍数出现，则输出 -1。

给定 $T$ 个测试用例，请分别解决它们。

以上为通义千问 qwen-max 翻译，仅供参考。

Problem Statement

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:

$K$

Output

Print $T$ lines. The $i$-th line should contain the answer for $\text{case}_i$.

Sample Input 1

4
1
7
10
999983

Sample 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 $10$.

update @ 2024/3/10 09:48:11