3 solutions did get invalidated because of this fixed test. Are random tests missing these edge cases?

Thanks, I fixed it.

All of the sample tests have the same message "Sample test failed for N=10, K=4".

Thank you. I've added sample tests and fixed tests.

Thank you. I've added the fixed test.

I don't think it is necessary. Everything works for K > N. Maybe there are should be some fixed tests with K > N.

Add more fixed tests and sample tests (perhaps you forgot to save/publish your change from the previous issue?)

should also add K <= N ?

• Tests with k = 1 should be removed from Random Tests: K = random.randint(1, 10**12) should be replaced with K = random.randint(2, 10**12) (don't forget Mini random tests also).

• The description should be updated: 2 <= K <= 10^12 (maybe it is better to use KaTeX and write: $2 \le K \le 10^{12}$).

• I also suggest to change the first sentence into "You are given a positive integer N and an integer K > 1."

Yeah okay, f(n,1) = n; I was already summing for all N.

The current definition doesn't work when $k=1$:

2. If it is divisible (always), divide the quotient by 1 again
3. If it is not divisible by 1 (never), end the operation.

From tests, $f(n, 1) = n$

Thank you. I've added more.

There should be more fixed tests (including tests with small k).

Isn't this a matter of defining f in a way that allows k = 1 ? Intuitively, f(n,1) = n * n+1 / 2.

Thank you, I have fixed it now.