Count K-Reducible Numbers Less Than N

Description

You are given a binary string s representing a number n in its binary form.

You are also given an integer k.

An integer x is called k-reducible if performing the following operation at most k times reduces it to 1:

- Replace x with the count of set bits in its binary representation.

For example, the binary representation of 6 is "110". Applying the operation once reduces it to 2 (since "110" has two set bits). Applying the operation again to 2 (binary "10") reduces it to 1 (since "10" has one set bit).

Return an integer denoting the number of positive integers less than n that are k-reducible.

Since the answer may be too large, return it modulo 109 + 7.