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`