John acquired a new game, "Destroying Asteroids". In this game, there is a grid with $$$R$$$ rows and $$$C$$$ columns. There is a spaceship located in row $$$0$$$ and column $$$0$$$. Each column from $$$1$$$ to $$$C$$$ has only one asteroid at height $$$c_i$$$. This means that if column $$$1$$$ has an asteroid at height $$$10$$$, then the asteroid is positioned in the grid at row $$$10$$$ and column $$$1$$$.

In the game, John can only move the spaceship within the same column, either upwards or downwards. When the spaceship moves upwards, it will be in row $$$r+1$$$, where $$$r$$$ is the previous row it was in before the movement. Conversely, if the spaceship moves downwards, it will be in row $$$r-1$$$, where $$$r$$$ is the current row before the movement.

In addition to moving the spaceship, John can press the beam button. When the beam button is pressed, the spaceship shoots a beam, which destroys all asteroids on the same row as the spaceship. The spaceship can shoot a maximum of $$$K$$$ times. The game ends when John has exhausted all his shots or there are no more asteroids left to destroy. The score John obtains is equal to the number of asteroids he destroyed with his shots in the level.

Since a level can be very challenging, John finds it difficult to achieve the maximum score in some levels. That's why he has asked for your help. Your task is to calculate the maximum score that John can obtain in a game level.