Number of Integers With Popcount-Depth Equal to K I

Description

You are given two integers n and k.

For any positive integer x, define the following sequence:

- p0 = x

- pi+1 = popcount(pi) for all i >= 0, where popcount(y) is the number of set bits (1's) in the binary representation of y.

This sequence will eventually reach the value 1.

The popcount-depth of x is defined as the smallest integer d >= 0 such that pd = 1.

For example, if x = 7 (binary representation "111"). Then, the sequence is: 7 → 3 → 2 → 1, so the popcount-depth of 7 is 3.

Your task is to determine the number of integers in the range [1, n] whose popcount-depth is exactly equal to k.

Return the number of such integers.