Raphael occasionally uses the subway system in the city of São Paulo and is now going to start using a ticket with a new fare scheme: a time-valid pass. When purchasing this type of ticket, one may choose a duration of $$$D$$$ days, with a cost of $$$C$$$ reais per day, resulting in a total cost of $$$D \cdot C$$$. With this ticket, the subway can be used freely for $$$D$$$ consecutive days (the day of purchase and the following $$$D-1$$$ days).

However, Raphael must take a ride-hailing service to reach the ticket office where this new type of pass is sold. Although online purchasing methods are available, Raphael prefers to pay in cash and receive a physical ticket. This ride has a cost of $$$K$$$ reais. Therefore, in practice, the total cost for Raphael to purchase a pass valid for $$$D$$$ days is $$$D \cdot C + K$$$ reais.

Raphael already knows the list of $$$N$$$ days on which he will need to use the subway, and he has asked for your help in determining the minimum possible cost that allows him to use the subway on all those days by purchasing only time-valid passes. Initially, Raphael does not own any valid ticket.

For example, suppose that $$$C = 3$$$, $$$K = 10$$$, and Raphael needs to use the subway on three days: 2 days from now, 3 days from now, and 8 days from now. One possible strategy would be to buy, 2 days from now, a pass valid for 7 days, resulting in a cost of $$$7 \cdot 3 + 10 = 31$$$. However, he could instead buy a pass valid for 2 days, 2 days from now, and another pass valid for 1 day, 8 days from now, resulting in a total cost of $$$(2 \cdot 3 + 10) + (1 \cdot 3 + 10) = 29$$$, which is therefore a cheaper option.