Given a binary string s and a positive integer n, return true if the binary representation of every integer from $1$ through n is a substring of s, or false otherwise.

A substring is a contiguous sequence of characters within a string.

Constraints:

• $1 \leq$ s.length $\leq 1000$

• s[i] is either '0' or '1'.

• $1 \leq$ n $\leq 10^9$

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.