Bulb Switcher II

There is a room with n bulbs labelled from 1 to n that all are turned on initially, and four buttons on the wall. Each of the four buttons has a different functionality:

• Button 1: Flips the status of all the bulbs.
• Button 2: Flips the status of all the bulbs with even labels (i.e., 2, 4, ...).
• Button 3: Flips the status of all the bulbs with odd labels (i.e., 1, 3, ...).
• Button 4: Flips the status of all the bulbs with a label j = 3k + 1 where k = 0, 1, 2, ... (i.e., 1, 4, 7, 10, ...).

You must make exactly presses button presses in total. For each press, you may pick any of the four buttons to press.

Given the two integers n and presses, return the number of different possible statuses after performing all presses button presses.