<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:
        def isValid(s):
            
            if int(s)% k == 0:
                # print(s)
                return True
            return False

        def getPerm(s):
            # print(s)
            dic = {}
            for i in s:
                if i in dic:
                    dic[i] += 1
                else:
                    dic[i] = 1
            
            res = math.factorial(len(s))
            for k,v in dic.items():
                res //= math.factorial(v)
            
            if '0' in dic:
                sub = math.factorial(len(s)-1)
                dic['0'] -= 1
                for k,v in dic.items():
                    sub //= math.factorial(v)
                res -= sub
            # print(res)
            return res

        visited = set()
        def solve(s):
            if len(s) == math.ceil(n/2):
                if n%2:
                    if isValid(s+s[:-1][::-1]):
                        t = s+s[:-1][::-1]
                        t = str(sorted(t))
                        # print(t)
                        if t not in visited:
                            cnt[0] += getPerm(s+s[:-1][::-1])
                            visited.add(t)
                else:
                    # if isValid(s+s[::-1]):
                    #     cnt[0] += getPerm(s+s[::-1])
                    if isValid(s+s[::-1]):
                        t = s+s[::-1]
                        t = str(sorted(t))
                        if t not in visited:
                            cnt[0] += getPerm(s+s[::-1])
                            visited.add(t)
                return
            if not s:
                for i in range(1,10):
                    solve(str(i))
            else:
                for i in range(10):
                    solve(s+str(i))
        
        cnt = [0]
        solve("")
        return cnt[0]
26484