In maths ( and Wikipedia ), this is called "partitioning".

I'm not here to complain and I really liked the Kata but I have some opinions about it and why I think it can be improved (and how to do it).

It's pointless test cases using numbers above MAX_SAFE_INTEGER in JavaScript.

Why?

1. A real solution using recursion breaks as 'max call stack' as it is pointed out by some users in comments
2. There's no point requiring use of BigInt and not cite it as required in Desciption (as long as I think this is not necessary)
3. This is a 7 kyu Kata. The user should not be concerned about performance that exceeds the MAX_SAFE_INTEGER

My suggestion is: I hardly recommed to maintain the range of numbers as

• 1 <= n <= 50
• 1 <= k <= 30

At least for JavaScript. JavaScript do not have full memory to store numbers like Python and if n exceeds 60, it easily surpass MAX_SAFE_INTEGER.

note: put a language specific note saying all results will be under MAX_DAFE_INTEGER, then, so that users don't try to use BigInt. Otherwise they'll still get the same error message.

Either test under MAX_SAFE_INTEGER or require BigInt results (but then existing solution will be invalidated). It is a "7 kyu" kata so testing under MAX_SAFE_INTEGER is a reasonable choice.

should i test only under the MAX_INTEGER what say?

It is not possible to solve this kata in JS with BigInt results. I get the following errors:

Fixed tests
expected {} to equal 1
Completed in 1ms
Random tests
expected {} to equal 7

I think it is possible to support both Number and BigInt results with a custom assertion. But I do not recommend to support Number results because these results are not precise for large input values.

BigInt has been added to support big numbers.

fixed

BigInt should be used in JavaScript:

Random tests
expected 1.7014118346044496e+38 to equal 1.7014118346044475e+38

Why you are testing values higher than MAX_SAFE_INTEGER in JS? This make no sense at all in this Kata as 7 kyu... Numbers above that are not precise and the values exceeds the time of execution or do not pass the tests.

If possible, can you make the test with numbers below MAX_SAFE_INTEGER in JS?

As a suggestion, I hardly recommed to maintain the range of numbers as:

• 1 <= n <= 50
• 1 <= k <= 30

At least for JS. JS do not have full memory to store numbers like Python and if n exceeds 60, it easily surpass MAX_SAFE_INTEGER.

Question

And how is this a kata issue?? You can ask questions under any specific solution, if that helps. Closing...

Edit: what the hell, sorry. It was showing up as issue to me. But you should use spoiler flag for questions like this.

You can search about fibonacci ladder problem where length of steps not greater than 2. Then think about generalization of this problem.