Statement

William is in charge of server provisioning for the Italian Team Olympiads, which essentially means that he has to make sure there are enough resources to sustain the load of users that connect during a contest. Today there is a contest (starting at second 0 and ending at second T) and it's important to spend as little as possible, so William wants to increase the server's power only when needed. We will assume for simplicity that: (1) When a user connects to the server, they will stay connected until the end of the contest. (2) If we pay k euro cent per second, then the server can sustain a load of at most k users per second. (3) At any integer second we can decide to increase the power (and the payment will increase from k euro cent per second to some other amount, greater than k). Since William will also have to supervise the contest, he will ask Giorgio to upgrade the server everytime an upgrade is needed. Upgrading the server is a very difficult and tiring operation...