<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 __init__(self):
        self.factorials = [1] * 11
        for i in range(1, 11):
            self.factorials[i] = self.factorials[i - 1] * i
    def getPals(self, n):
        palindromes = []
        if n == 0:
            return palindromes
        
        half_length = (n + 1) // 2
        start = 10 ** (half_length - 1)
        end = 10 ** half_length - 1
        if n == 1:
            start = 0
        
        for first_half in range(start, end + 1):
            str_half = str(first_half)
            if n % 2 == 0:
                str_pal = str_half + str_half[::-1]
            else:
                str_pal = str_half + str_half[:-1][::-1]
            if len(str_pal) == n:
                palindromes.append(int(str_pal))
                
        return palindromes

    def countGoodIntegers(self, n: int, k: int) -> int:
        def solve(number):
            total = 0
            for d in "123456789":
                c= Counter(number)
                if c[d] == 0:
                    continue
                c[d]-=1
                if c[d]<0: break
                fact = self.factorials[n - 1]
                for i in "0123456789":
                    fact //= self.factorials[c[i]]
                total += fact
            return total
            
        valid_palindromes = [str(num) for num in self.getPals(n) if num % k == 0]
        ans= 0
        uni = set()
        for num in valid_palindromes:
            uni.add(tuple(sorted(num)))
        return sum(solve(num) for num in uni)

26750