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

<ul>
	<li>Every song is played <strong>at least once</strong>.</li>
	<li>A song can only be played again only if <code>k</code> other songs have been played.</li>
</ul>

<p>Given <code>n</code>, <code>goal</code>, and <code>k</code>, return <em>the number of possible playlists that you can create</em>. Since the answer can be very large, return it <strong>modulo</strong> <code>10<sup>9</sup> + 7</code>.</p>
<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

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

<p><strong class="example">Example 2:</strong></p>

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

<p><strong class="example">Example 3:</strong></p>

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

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= k &lt; n &lt;= goal &lt;= 100</code></li>
</ul>

class Solution {
public:
    int N;
    int GOAL;
    int K;
    long t[101][101];
    const int MOD = 1e9+7;
    
    long solve(int count_song, int count_unique) {
        if(count_song == GOAL) {
            if(count_unique == N)
                return 1;
            
            return 0;
        }
        
        if(t[count_song][count_unique] != -1)
            return t[count_song][count_unique];
        
        long result = 0;
        
        //Option-1 (Play a unique song)
        if(count_unique < N)
            result += (N-count_unique) * solve(count_song+1, count_unique+1);
        
        //Option-2 (Replay a song)
        if(count_unique > K)
            result += (count_unique - K) * solve(count_song+1, count_unique);
        
        
        return t[count_song][count_unique] = result % MOD;

    }
    
    int numMusicPlaylists(int n, int goal, int k) {
        N    = n;
        GOAL = goal;
        K    = k;
        memset(t, -1, sizeof(t));
        return solve(0, 0); 
    }
};
7500