You are given a binary string s and a positive integer k.

In a single operation, you can select any substring of s of length k and invert all of its bits, replacing every $'0'$ with a $'1'$ and every $'1'$ with a $'0'$. This operation can be applied any number of times.

Return the number of distinct binary strings that can be produced. Since the result can be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ k $\leq$ s.length $\leq 10^5$

• s[i] is either $'0'$ or $'1'$.

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.