<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,GOAL, K;
    long long MOD=1e9+7;
    int  dp[1001][1001];
    long long  solve(  int songs, int unique){
        if( songs==GOAL){
   if(unique==N) return 1;
      return 0;
            

        }
  if( dp[songs][unique]!=-1) return dp[songs][unique];
long long result=0;
   // play unique song
   // if unique< N
   if(unique<N)
         result+=(( N-unique) *solve( songs+1, unique+1))%MOD;
if(unique> K) // repaly the song 
             result+=(( unique-K) *solve( songs+1, unique))%MOD;
         
      return dp[songs][unique]=result%MOD;


    }
    int numMusicPlaylists(int n, int goal, int k) {

        N=n;
        GOAL=goal;
        K=k;
memset(dp,-1,sizeof(dp));
         return solve(0,0);




        
    }
};
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