0672. Bulb Switcher II

https://leetcode.com/problems/bulb-switcher-ii

Description

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

Example 4:

**Input:** n = 1, presses = 0
**Output:** 1
**Explanation:** Status can only be [on] since you cannot press any of the buttons.

Example 5:

**Input:** n = 1, presses = 2
**Output:** 2
**Explanation:** Status can be:
- [off] by pressing button 1 then button 1 again
- [on] by pressing button 1 then button 2

Constraints:

• 1 <= n <= 1000

• 0 <= presses <= 1000

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