Statement

Giorgio loves reading before going to sleep, but today he's not at home but in a cheap hotel abroad for a conference. In the Crazy Lights hotel, each room has N lights and the corresponding N buttons; if you press the i-th button and the i-th light was off, it will immediately turn on! Now Giorgio is in the bed and he wants to start reading: he needs to switch off all the lights but the K-th. There is an odd behaviour though: he noticed that by using the i-th button not only the i-th light turns on but also some other lights turn off! He spent a few minutes to map all the switches to the lights and now he knows exactly what each button does. The management told Giorgio to never use the i-th button if the i-th light is already on, otherwise there will be a peak of power and all the hotel will go black! Help Giorgio, who wants to start reading as soon as possible: which is the minimum number of buttons to press in order to switch off all the lights but the K-th one?