672 - Bulb Switcher II\.

Medium

There is a room with n bulbs labeled 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 where:

• 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.

Example 1:

Input: n = 1, presses = 1

Output: 2

Explanation: Status can be:

• off by pressing button 1

• on by pressing button 2

Example 2:

Input: n = 2, presses = 1

Output: 3

Explanation: Status can be:

• off, off by pressing button 1

• on, off by pressing button 2

• off, on by pressing button 3

Example 3:

Input: n = 3, presses = 1

Output: 4

Explanation: Status can be: - off, off, off by pressing button 1 - off, on, off by pressing button 2 - on, off, on by pressing button 3 - off, on, on by pressing button 4

Constraints:

• 1 <= n <= 1000

• 0 <= presses <= 1000