<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 k, n, g;
    vector<vector<int>> dp = vector<vector<int>>(101, vector<int>(101, -1));
    int MOD = 1e9 + 7;

    int solve(int cntsong, int cntunq) {
        if (cntsong == g) {
            if (cntunq == n) return 1;
            return 0;
        }
        if (dp[cntsong][cntunq] != -1) {
            return dp[cntsong][cntunq];
        }
        long long p = 0, q = 0;

        if (cntunq < n) {
            p = ((long long)(n - cntunq) * solve(cntsong + 1, cntunq + 1)) % MOD;
        }

        if (cntunq > k) {
            q = ((long long)(cntunq - k) * solve(cntsong + 1, cntunq)) % MOD;
        }

        return dp[cntsong][cntunq] = (p + q) % MOD;
    }

    int numMusicPlaylists(int n, int goal, int k) {
        this->k = k;
        this->n = n;
        this->g = goal;
        fill(dp.begin(), dp.end(), vector<int>(101, -1)); 

        return solve(0, 0);
    }
};

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