<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:
        gset=set()
        count=0
        s=[]
        fact=[0]*11
        fact[0] = 1
        for i in range(1, 11):
            fact[i] = (fact[i - 1] * i)



        def solve(sz,p):
            nonlocal s,n,k,count
            if sz==0:
                cmod= "".join(list(map(str,s)))
                if n%2:
                    cmod=cmod[:n//2]+cmod[::-1]
                else:
                    cmod=cmod+cmod[::-1]
                if int(cmod)%k:return
                temp=tuple(sorted(list(cmod)))
                if temp in gset:return
                gset.add(temp)
                d=defaultdict(lambda :0)
                for ele in cmod:
                    d[int(ele)]+=1
                dd=[[i,d[i]] for i in d]
                ways= fact[n-d[0]] * fact[n-1]/(fact[d[0]]*fact[n-d[0]-1])
                for ele in d:
                    if ele==0:continue
                    ways/=fact[d[ele]]
                count+=int(ways)
                return

            for i in range(p,10):
                s.append(i)
                solve(sz-1,0)
                s.pop()

        

        solve((n+1)//2,1)
        return int(count)
        
22490