Given a positive integer k, find the length of the smallest positive integer n such that n is divisible by k, and n contains only the digit $1$ in its decimal representation.

Return the length of n. If no such integer n exists, return $-1$.

Constraints:

• $2 \leq$ k $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.