CF853A Planning

Helen works in Metropolis airport. She is responsible for creating a departure schedule. There are $ n $ flights that must depart today, the $ i $ -th of them is planned to depart at the $ i $ -th minute of the day. Metropolis airport is the main transport hub of Metropolia, so it is difficult to keep the schedule intact. This is exactly the case today: because of technical issues, no flights were able to depart during the first $ k $ minutes of the day, so now the new departure schedule must be created. All $ n $ scheduled flights must now depart at different minutes between $ (k+1) $ -th and $ (k+n) $ -th, inclusive. However, it's not mandatory for the flights to depart in the same order they were initially scheduled to do so — their order in the new schedule can be different. There is only one restriction: no flight is allowed to depart earlier than it was supposed to depart in the initial schedule. Helen knows that each minute of delay of the $ i $ -th flight costs airport $ c_{i} $ burles. Help her find the order for flights to depart in the new schedule that minimizes the total cost for the airport.

The first line contains two integers $ n $ and $ k $ ( $ 1

The first line must contain the minimum possible total cost of delaying the flights. The second line must contain $ n $ different integers $ t_{1},t_{2},...,t_{n} $ ( $ k+1

Let us consider sample test. If Helen just moves all flights $ 2 $ minutes later preserving the order, the total cost of delaying the flights would be $ (3-1)·4+(4-2)·2+(5-3)·1+(6-4)·10+(7-5)·2=38 $ burles. However, the better schedule is shown in the sample answer, its cost is $ (3-1)·4+(6-2)·2+(7-3)·1+(4-4)·10+(5-5)·2=20 $ burles.