You are given a binary string s representing a positive integer n in its binary form, and an integer k.

In a single operation, an integer is replaced by the count of set bits in its binary representation. An integer is considered $k$ reducible if it can be reduced to $1$ in at most $k$ operations.

Return the count of positive integers strictly less than n that are $k$ reducible. Since the answer may be large, return it modulo $10^9 + 7$.

Constraints:

• $1 \leq$ s.length $\leq 800$

• s has no leading zeros.

• s consists only of the characters $'0'$ and $'1'$.

• $1 \leq$ k $\leq 5$

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.