<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:
        p10mk = [1]*n
        for i in range(1,n):
            p10mk[i] = (p10mk[i-1]*10)%k
        self.palins = set()
        m = (n+1)//2
        def getPalin(root,n):
            if len(root) == n//2:
                return root + root[::-1]
            return root + root[:-1][::-1]
        def dfs(i,r,root):
            if i == m:
                if r == 0:
                    self.palins.add(getPalin(root,n))
                return
            for d in range(10):
                if i == 0 and d == 0:
                    continue
                if n%2 and i == n-1-i:
                    r2 = (r+d*p10mk[i])%k
                else:
                    r2 = (r+d*p10mk[i]+d*p10mk[n-1-i])%k
                dfs(i+1,r2,root+str(d))
        dfs(0,0,"")
        #print(self.palins)
        def rearrange(x):
            return "".join(sorted(list(x)))
        self.palins = set(rearrange(x) for x in self.palins)
        def recon(s,c):
            res = []
            ok = False
            for c1 in s:
                if c1 == c and not ok:
                    ok = True
                else:
                    res.append(c1)
            return "".join(res)
        def getCnt(s,l0r):
            digit_c = collections.Counter(s)
            if l0r:
                res = 0
                for k in digit_c:
                    if k == "0":
                        continue
                    res += getCnt(recon(s,k),False)
            else:
                total = sum(v for v in digit_c.values())
                res = 1
                for v in digit_c.values():
                    res *= math.comb(total,v)
                    total -= v
            return res
        return sum(getCnt(s,True) for s in self.palins)
30211