<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 long dp[201][201];
int m=1e9+7;

long  fun(int i,int j,int k,int g)
{
    if(i==0)
  {  long long ans=1;
   for(int l=0;l<k;l++)
   { ans=ans*((long long)(j-g));
    ans%=m;}
    return ans;}
    if(k==0)
    return 0;
    if(dp[i][k]!=-1)return dp[i][k];
    long long ans=1;
    if(j-i>g)
    {
        ans=(i)*fun(i-1,j,k-1,g);
        ans%=m;

        ans+=max(j-i-g,0)*fun(i,j,k-1,g);
        ans%=m;
    }
    else
     ans=(i)*fun(i-1,j,k-1,g);
     ans%=m;
return dp[i][k]=ans;
}
    int numMusicPlaylists(int n, int goal, int k) {
        memset(dp,-1,sizeof(dp));
        return fun(n,n,goal,k);
    }
};
7700