Your music player contains `n` different songs. You want to listen to `goal` songs (not necessarily different) during your trip. To avoid boredom, you will create a playlist so that:

- Every song is played at least once.
- A song can only be played again only if `k` other songs have been played.

Given `n`, `goal`, and `k`, return the number of possible playlists that you can create. Since the answer can be very large, return it modulo `109 + 7`.

Example 1:

    Input: n = 3, goal = 3, k = 1
    Output: 6
    Explanation: There are 6 possible playlists: [1, 2, 3], [1, 3, 2], [2, 1, 3], [2, 3, 1], [3, 1, 2], and [3, 2, 1].

Example 2:

    Input: n = 2, goal = 3, k = 0
    Output: 6
    Explanation: There are 6 possible playlists: [1, 1, 2], [1, 2, 1], [2, 1, 1], [2, 2, 1], [2, 1, 2], and [1, 2, 2].

Example 3:

    Input: n = 2, goal = 3, k = 1
    Output: 2
    Explanation: There are 2 possible playlists: [1, 2, 1] and [2, 1, 2].

Constraints:

- `0 <= k < n <= goal <= 100`