Statement

Fearsome William is still free, and the Police is searching him in Murder Boulevard! This street is L meters long, and currently William is at x=0, trying to reach his nest at x=L. Along this street there are N semaphores at positions X_i. All the traffic lights are synchronized: at t=0 the green triggers, and will stay green for T seconds; at t=T the red triggers, and will stay red for T seconds; and then the cycle repeats. William wants to reach his nest as quickly as possible, but he doesn't want to attract too much attention. Therefore, he travels at a constant speed of 1 meter per second (the speed limit), and he will stop and wait if he's at a red semaphore. Since he's very impatient, sometimes he may cross the red semaphore without waiting for the green, but he can do so at most R times. Which is the least amount of time William needs to reach his nest?