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:
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