672. Bulb Switcher II
Medium
118
179

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`
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