There is a room with n bulbs labeled from $1$ to n, all initially turned on. You are also given four buttons that can perform the following operations:

• Button $1$: Flips the state of all bulbs.

• Button $2$: Flips the state of bulbs with even labels (i.e., $2, 4, 6, \dots$).

• Button $3$: Flips the state of bulbs with odd labels (i.e., $1, 3, 5, \dots$).

• Button $4$: Flips the state of bulbs with labels of the form $3k + 1$ for $k \geq 0$ (i.e., $1, 4, 7, 10, \dots$).

Given the two integers n and presses, return the number of distinct possible configurations of all n bulbs after pressing any of the buttons exactly presses times.

Constraints:

• $1 \leq$ n $\leq 1000$

• $0 \leq$ presses $\leq 1000$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.