How to dynamically/recursively add columns to generate permutations..

Hello,

I am working on generating permutations for a specific applications. Basically the problem is there are N steps (24 as of now but can change) and at each step there is a decision to be made. And based on this decision I will be making a calculation.  And the maximum number of decisions that can be made is also a parameter. (k) 

So for N = 4, k=1 the possibilities are;

0000
0001
0010
0100
1000

And for N=4, k=2 the possibilities are; so k=n includes k=n-1...

0000
0001
0010
0100
1000
0011
0101
0110
1001
1010
1100

I thought (not verified) the fastest way to generate the k=1 values is to generate a list of values 2^0...2^N and convert them to binary if I need a visual representation.

decisionslist1 = = Table.FromList(List.Generate(()=>[x = 0, y=0],each [x] <= N, each [x=[x]+1,y=Number.Power(2,x-1)],each [y]), Splitter.SplitByNothing(), null, null, ExtraValues.Error)

decimal - binary
0        0000
1        0001
2        0010
4        0100
8        1000

And then for k=2 (and potentiallyfor all the next k) a sensible approach seemed to cartesian product the previous list with itself add the values and eliminate duplicates.

I could write the code for k=2 but I can't figure out a way to make it generic, which I think requires dynamically adding columns or recursion.

let
    N = 4,
    decisionslist1 = Table.FromList(List.Generate(()=>[x = 0, y=0],each [x] <= N, each [x=[x]+1,y=Number.Power(2,x-1)],each [y]), Splitter.SplitByNothing(), null, null, ExtraValues.Error),
    cartesian = Table.AddColumn(decisionslist1, "Custom", each decisionslist1),
    expanded = Table.ExpandTableColumn(cartesian, "Custom", {"Column1"}, {"Column1.1"}),
    renamed = Table.RenameColumns(expanded,{{"Column1", "a"}, {"Column1.1", "b"}}),
    select = Table.SelectRows(renamed,each ([a] <> [b]) or (Number.From([a]) = 0 and Number.From([b])=0)),
    sum = Table.AddColumn(select, "Custom", each [a]+[b]),
    removeDuplicates = Table.Distinct(sum, {"Custom"}),
    decisionlist2 = Table.RemoveColumns(removeDuplicates,{"a", "b"})
in
    decisionlist2

outputing 

decimal - binary
0         0000
1         0001
2         0010
4         0100
8         1000
3         0011
5         0101
9         1001
6         0110
10        1010
12        1100

How can I convert this into a generic function does this k-1 times taking k as an input? 

I understand power query is not the ideal environment for such work but I am unfortunately there...

Thank you

Ruchan Ziya