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 + 1wherek = 0, 1, 2, ...(i.e.,1, 4, 7, 10, ...). You must make exactlypressesbutton 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 <= 10000 <= presses <= 1000