<p>You are given two <strong>positive</strong> integers <code>n</code> and <code>k</code>.</p>

<p>An integer <code>x</code> is called <strong>k-palindromic</strong> if:</p>

<ul>
	<li><code>x</code> is a <span data-keyword="palindrome-integer">palindrome</span>.</li>
	<li><code>x</code> is divisible by <code>k</code>.</li>
</ul>

<p>An integer is called <strong>good</strong> if its digits can be <em>rearranged</em> to form a <strong>k-palindromic</strong> integer. For example, for <code>k = 2</code>, 2020 can be rearranged to form the <em>k-palindromic</em> integer 2002, whereas 1010 cannot be rearranged to form a <em>k-palindromic</em> integer.</p>

<p>Return the count of <strong>good</strong> integers containing <code>n</code> digits.</p>

<p><strong>Note</strong> that <em>any</em> integer must <strong>not</strong> have leading zeros, <strong>neither</strong> before <strong>nor</strong> after rearrangement. For example, 1010 <em>cannot</em> be rearranged to form 101.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 3, k = 5</span></p>

<p><strong>Output:</strong> <span class="example-io">27</span></p>

<p><strong>Explanation:</strong></p>

<p><em>Some</em> of the good integers are:</p>

<ul>
	<li>551 because it can be rearranged to form 515.</li>
	<li>525 because it is already k-palindromic.</li>
</ul>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 1, k = 4</span></p>

<p><strong>Output:</strong> <span class="example-io">2</span></p>

<p><strong>Explanation:</strong></p>

<p>The two good integers are 4 and 8.</p>
</div>

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

<div class="example-block">
<p><strong>Input:</strong> <span class="example-io">n = 5, k = 6</span></p>

<p><strong>Output:</strong> <span class="example-io">2468</span></p>
</div>

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

<ul>
	<li><code>1 &lt;= n &lt;= 10</code></li>
	<li><code>1 &lt;= k &lt;= 9</code></li>
</ul>

MYANS = [[0, 0, 0, 0, 0, 0, 0, 0, 0, 0], [0, 9, 4, 3, 2, 1, 1, 1, 1, 1], [0, 9, 4, 3, 2, 1, 1, 1, 1, 1], [0, 243, 108, 69, 54, 27, 30, 33, 27, 23], [0, 252, 172, 84, 98, 52, 58, 76, 52, 28], [0, 10935, 7400, 3573, 4208, 2231, 2468, 2665, 2231, 1191], [0, 10944, 9064, 3744, 6992, 3256, 3109, 3044, 5221, 1248], [0, 617463, 509248, 206217, 393948, 182335, 170176, 377610, 292692, 68739], [0, 617472, 563392, 207840, 494818, 237112, 188945, 506388, 460048, 69280], [0, 41457015, 37728000, 13726509, 33175696, 15814071, 12476696, 36789447, 30771543, 4623119], [0, 41457024, 39718144, 13831104, 37326452, 19284856, 13249798, 40242031, 35755906, 4610368]]

class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        return MYANS[n][k]
16633