The problem is decided by a word RAM program that reads the word, with $n$ clients and $m$ days, and tests whether it is at least $2 ^ (2 n² + n + 3) + 2$ long, by doubling a counter held at the length. If it is, and the fairness parameter is at most $m$, the program writes the word of an integer program with $2 ^ (n² + n) + n$ variables: one per pair of a type of day (its conflict relation) and a set of clients, which the pair says run together on the days of that type, and one slack per client; one constraint fixes, for each type, the number of days of that type, and one says, for each client, that the days it is not served on are at most $m - k$. It then chooses a word length $w'$ for which that word fits, and runs the program that solves the integer programs of the family ($IlpClients.ilpClients_fpt$, proved) on it at that word length, by an interpreter of word RAM programs written in the IMP+ language, the memory of the interpreted machine being an array of 2 ^ w' cells. The program is read as data, so it is the same for every word length. If the word is too short, the number of schedules is at most a function of $n$ alone, and the program enumerates them. A parameter above $m$ is answered $no$ at once when there is a client. No result is cited.