Statement

Marco has recently founded a startup company with N employees. When hiring, he promised to equally split a productivity prize of E euros across the best employees, if the company managed to get some conspicuous EU funds. Unexpectedly, the company was funded, and now he has to keep to his word! However, Marco would very much prefer to award most of the E euros to himself. There is only one parameter he can leverage towards this end: the number of employees to award. He can choose any number K of employees, between a minimum of M (the employees directly involved in getting the funds) and a maximum of N (all employees). By choosing K wisely, some of the E euros may be left for him: since he promised to split the prize equally, he can always take the remainder of the division for himself! For example, assume that E = 100\euro and there are N = 9 employees, out of which M = 7 directly participated in the funding process...