Number of Music Playlists
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
kother 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 10^9 + 7.
Example 1
Input
n = 3, goal = 3, k = 1Output
6There 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 = 0Output
6There are 6 possible playlists: [1, 1, 2], [1, 2, 1], [2, 1, 1], [2, 2, 1], [2, 1, 2], and [1, 2, 2].
Constraints
- 0 <= k < n <= goal <= 100