<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:
        factorial = [1, 1]
        for i in range(2, 11):
            factorial.append(factorial[i-1] * i)

        def create_palindrome(num, even, x):
            num = str(num)
            num = '0' * (x-len(num)) + num
            if even:
                num = num[::-1] + num
            else:
                num = num[::-1] + num[1:]
            return int(num)

        def num_possibles(palindrome):
            count = dict()
            len_palindrome = len(palindrome)
            for c in palindrome:
                count.setdefault(c, 0)
                count[c] += 1

            lead_zeros = 1
            if '0' in count:
                len_palindrome -= count['0']
                lead_zeros = factorial[len(palindrome) - 1] // (factorial[count['0']] * factorial[len(palindrome) - 1 - count['0']])

            result = factorial[len_palindrome]
            for c in count:
                if c != '0':
                    result //= factorial[count[c]]

            return result * lead_zeros

        even = False
        if n % 2 == 0:
            even = True
        x = n//2 + (0 if even else 1)
        generated_palindromes = set()
        for i in range(1, 10**x):
            palindrome = create_palindrome(i, even, x)
            if palindrome % k == 0:
                generated_palindromes.add(str(palindrome))
        generated_palindromes = [
            palindrome for palindrome in generated_palindromes
            if len(palindrome) == n
        ]

        dedup_generated_palindromes = list()
        dup_palindrome = set()
        for palindrome in generated_palindromes:
            x = list(palindrome)
            x.sort()
            x = ''.join(x)
            if x not in dup_palindrome:
                dedup_generated_palindromes.append(palindrome)
                dup_palindrome.add(x)

        total = 0
        for palindrome in dedup_generated_palindromes:
            total += num_possibles(palindrome)
        return total
28614