Water Sort Puzzle (Challenge)

Chef wants to study reactions between non-miscible reagent samples with different colours. There are $N$ colours (numbered $1$ through $N$). Chef has $N+2$ test tubes (numbered $1$ through $N+2$), each of them can hold a volume $M$ ml; initially, tubes $N+1$ and $N+2$ are empty, while for each $i$ ($1 \le i \le N$), the $i$-th tube is completely filled and contains $M$ ml of reagents with some col