3352 - Count K-Reducible Numbers Less Than N.

Hard

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 <code>10⁹ + 7</code>.

Example 1:

Input: s = "111", k = 1

Output: 3

Explanation:

n = 7. The 1-reducible integers less than 7 are 1, 2, and 4.

Example 2:

Input: s = "1000", k = 2

Output: 6

Explanation:

n = 8. The 2-reducible integers less than 8 are 1, 2, 3, 4, 5, and 6.

Example 3:

Input: s = "1", k = 3

Output: 0

Explanation:

There are no positive integers less than n = 1, so the answer is 0.

Constraints:

• 1 <= s.length <= 800

• s has no leading zeros.

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

• 1 <= k <= 5