>>129
Nice, I treat the fact that our results are the same as a miracle because I always get something wrong during calculations. x)

Also I wonder if determining number for arbitrary word and \math{n} (or just equation for \math{K_k, k \in 1,...,n}) can have an elegant equation or generic brute-force algorithm is the best way. 

For example the word SUS is kinda sus, because SUSUSUSx is a valid id with three occurences of the searched word. 

We can assume that there are problems when \math{k}-long suffix of the word is \math{k}-long prefix like when 'S' is 1-long suffix and prefix of 'SuS' and I see hope there, but words like 'SSUSSUSS' have the same words of length 1,2 and 5 as prefixes and suffixes of respective lengths.