A die simulator rolls a die with $6$ faces, numbered from $1$ to $6$.

You are given an integer n and an integer array rollMax of length $6$, where rollMax[i] specifies the maximum number of consecutive times the face $i + 1$ can appear in any valid sequence of rolls.

Return the total number of distinct valid sequences of length n that can be generated. Since the answer may be very large, return it modulo $10^9 + 7$.

Note: Two sequences are considered distinct if they differ at at least one position.

Constraints:

• $1 \leq$ n $\leq 5000$

• rollMax.length $= 6$

• $1 \leq$ rollMax[i] $\leq 15$

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.