<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:
    @staticmethod
    def _getPalindromes(start):
            pals = defaultdict(list)
            num = start
            while True:
                s = str(num)
                l = len(s)
                if l > 10:
                    break
                s = ''.join(chain(s[:l//2+l%2], reversed(s[:l//2])))
                # s = s[:l//2+l%2] + s[l//2-1::-1]
                num = int(s)
                pals[len(s)].append(num)
                
                num += 10**(l//2)
            
            return pals

    pals = _getPalindromes(0)
    mem = {}

    def countGoodIntegers(self, n: int, k: int) -> int:
        if n == 1:
            return sum(q%k == 0 for q in range(1, 10))


        def getPalindromes(start):
            num = start
            while True:
                s = str(num)
                l = len(s)
                s = ''.join(chain(s[:l//2+l%2], reversed(s[:l//2])))
                # s = s[:l//2+l%2] + s[l//2-1::-1]
                num = int(s)
                if num >= start:
                    yield num
                
                num += 10**(l//2)
        

        def perm():
            if not any(z.values()):
                return 1
            
            res1 = 0
            for ch in z:
                if z[ch]:
                    z[ch] -= 1
                    res1 += perm()
                    z[ch] += 1
            
            return res1

        
        seen = set()
        res = 0
        #for pal in getPalindromes(int('1'+'0'*(n-2)+'1')):
        for pal in self.pals[n]:
            s = str(pal)
            
            if len(s) > n:
                break
            
            if pal%k != 0:
                continue
            
            t = ''.join(sorted(s))
            if t in seen:
                continue
            seen.add(t)
            
            #print(pal)
            z = Counter(s)
            q = (z['0'], tuple(sorted(z.values())))
            if q not in self.mem:
                cnt = 0
                for ch in z:
                    if ch == '0':
                        continue
                
                    z[ch] -= 1
                    cnt += perm()
                    z[ch] += 1
            
                self.mem[q] = cnt

            res += self.mem[q]
            
        return res
25685