Statement

By selling his marvellous mega-mansion, Edoardo was able to cover the OIS deficit and even save some money to build a more humble replacement. However, the only affordable way left is to use some of the N discounted prefabricated columns of length L_i available from exhausting stocks. These columns may be used for their exact length L_i, or may be combined in pairs (i,j) to produce a single column of length L_i + L_j. Combining more than two columns together is never allowed for safety reasons. The new OIS building will require M columns each of the same height H (produced from one or two of the available prefabricated columns). This height has to to be at least T in order to fit all the workers and equipments, and of course, the smaller the building, the cheaper the final price. Help Edoardo determine the minimal height H for which a working building can be made!