A company operates N shops, selling M different products in each shop. The company
has a large depot where the products are packed before delivering to shops. Each shop
receives the same number of items of each product. Hence the company packs a certain
number of items of a given product into a container, and labels that container with the
product identifier. Products are identified by the numbers from 1 to M. Thus, at the end of
packing, there are N*M containers in the depot, and exactly N containers are labeled with a
given product label for each product. Because the depot is in a narrow building, the
containers are arranged in a single row. In order to speed-up distribution, the manager of
the depot wants to rearrange the containers. Since the product delivery to the shops occurs
by sending exactly one truck to each shop, and each truck carries one container of each
product, a suitable arrangement is the following. The first M containers in the row must be
labeled with different product labels, the second M containers in the row must be labeled
with different product labels, and so on. Unfortunately, there is only one free place at the
end of the row to hold a container. Therefore the rearrangement must be performed by
successively picking up a container and moving it to the free place. After the rearrangement
the free place must be at the end of the row.

The goal is to achieve the required rearrangement by a minimal number of moves.