Do you need an algorithm for splitting a natural number n into m parts (zeros are also included) or at least a sketch?

Question

Mathematics

There is an algorithm, but it is not understandable and not intelligible:
Generation of compositions of a natural number n by a given rank m means: split n into m non-negative integer terms in all possible ways.
In other words, to split n successively written ones into a given number m of parts in all possible ways (empty parts are also allowed).
If zeros are chosen as separator characters, then m parts are generated by m-1 separators, i.e. m-1 with zeros. Thus, the task is reduced to enumeration of bit strings of length q=n+m-1, filtering out those in which the number of zeros is different from m-1.
As an auxiliary algorithm, we need an algorithm for generating all binary sequences of length q.
The bit array b[q], b[q-1], ..., b[0] is used, which is first set to zero.
The generated sequence is written b[q-1], ..., b[0], b[q] - for technical purposes only: the generating loop ends as soon as b[q] becomes equal to 1.
while b[q] =0 do
begin
1. print the sequence b[q-1], ..., b[0];
2. find the first zero element b[i] from right to left and replace it with one, and erase all elements to the right of it to zero.
end