You have n different songs and want to create a playlist of length goal.

A playlist is considered valid if:

• Every song is played at least $1$ time.

• A song can only be played again if at least k other songs have been played after its previous occurrence.

Given n, goal, and k, return the total number of possible playlists. Since the answer can be very large, return it modulo $10^9 + 7$.

Constraints:

• $0 \leq$ k $<$ n $\leq$ goal $\leq 100$

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.