<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>

class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        from collections import Counter
        tmp = []
        if n%2==0:
            for i in range(10**(n//2)):
                if i%10==0:
                    continue
                s = str(i).zfill(n//2)
                s = "".join(reversed(s)) + s
                x = int(s)
                tmp.append(x)
        else:
            for i in range(10**(n//2 + 1)):
                if i%10==0:
                    continue
                s = str(i).zfill(n//2 + 1)
                s = "".join(reversed(s[1:])) + s
                x = int(s)
                tmp.append(x)
        s = set()
        for t in tmp:
            if t%k==0:
                l = sorted(Counter(map(int,list(str(t)))).most_common())
                s.add(tuple(l))
        ans = 0
        factorial = [1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880, 3628800]
        def func(l: list[tuple[int,int]]) -> int:
            p = 1
            t = 0
            for i,j in l:
                p *= factorial[j]
                t += j
            return factorial[t]//p

        for l in s:
            l = list(l)
            x = func(l)
            if l[0][0]==0:
                l[0]=(0,l[0][1]-1)
                x -= func(l)
                l[0]=(0,l[0][1]+1)
            ans += x
        return ans
23289