Not All Flavours

Chef made $N$ pieces of cakes, numbered them $1$ through $N$ and arranged them in a row in this order. There are $K$ possible types of flavours (numbered $1$ through $K$); for each valid $i$, the $i$-th piece of cake has a flavour $A_i$. Chef wants to select a contiguous subsegment of the pieces of cake such that there is at least one flavour which does not occur in that subsegment. Find the ma