Each spectator thought he would get $K-P+1$ pieces of walnut roll (that is how many pieces there are in total, marked from $P$ to $K$). The solution to the first part of the task is therefore determining the maximum value of $K-P+1$ which we calculate for each spectator individually.

As spectators were taking pieces of the walnut roll, at some point it might have occurred that a spectator could not take a piece that was provided for them because someone else had taken it already. We therefore create an array of a maximum length of $1000$ where we initialize every element to the value $1$ (every piece is in its place). For each spectator marked with $i$, we sum up the values in the array marked from $P_i$ to $K_i$; also, in that interval, we change every value $1$ to $0$ (the piece is not there anymore). During this procedure, we keep the maximum value of the sum.