A self-dividing number is an integer that is divisible by every digit it contains. For example, $128$ is a self-dividing number because $128$ is divisible by $1$, $2$, and $8$.

A self-dividing number cannot contain the digit $0$.

Given two integers left and right, return a list of all the self-dividing numbers in the range $[$left, right$]$ in inclusive order.

Constraints:

• $1 \leq$ left $\leq$ right $\leq 10^4$

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.