<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:
     long N,GOAL,K;
     long v[301][301];
     long mod=1e9+7;
     long solve(int count_song, int count_unique)
     {
        if(count_song == GOAL)
        {
            return count_unique == N ? 1: 0;
        }

        if(v[count_song][count_unique] != -1)
        {
            return v[count_song][count_unique];
        }
        long result=0;


        //option 1 :: (play a unique)
        if(count_unique  < N)
        {
            result+=(N - count_unique)*solve(count_song+1,count_unique+1);
            result%=mod;

        }
        

        //option 2 :: (Replay a song)
        if(count_unique > K)
        {
            result+=(count_unique - K)*solve(count_song+1,count_unique);
            result%=mod;

        }
        
        return v[count_song][count_unique]=result;


     }
    int numMusicPlaylists(int n, int goal, int k) {
        N=n;
        GOAL=goal;
        K=k;


        memset(v,-1,sizeof(v));

        return (int) solve(0,0);
        
    }
};
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