<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>

from collections import deque
from collections import Counter
class Solution:
    def countGoodIntegers(self, n: int, k: int) -> int:
        #hm of digits
        #encode digits as keys in a set
        #print({0,2} == {2,0})
        sevenMods = [10**i % k for i in range(n)]
        self.palset = set()
        def getSev(sevenMods, digs, rem, num):
            if digs[0] == -1:
                digit_count = Counter(num)
               
                self.palset.add(tuple(sorted(digit_count.items())))
                return
            if digs[0] == digs[1]:
                for i in range(10):
                    
                    newrem = (rem + i*sevenMods[digs[0]])%k
                    if digs[0] != 0 or (i != 0 and newrem == 0):
                    
                        num.append(i)
                        getSev(sevenMods, (digs[0]-1, digs[1]+1), newrem, num)
                        num.pop()
                
            else:
                for i in range(10):
                    newrem = (rem + i*sevenMods[digs[0]] + i*sevenMods[digs[1]])%k
                    if digs[0] != 0 or (i != 0 and newrem == 0):
                        num.append(i)
                        num.appendleft(i)
                        getSev(sevenMods, (digs[0]-1, digs[1]+1), newrem, num)
                        num.pop()
                        num.popleft()
        
        
        getSev(sevenMods, ((n-1)//2, n//2), 0, deque([]))
        res = 0
        for counts in self.palset:  
            
            tot = factorial(n)
            ztimes = 0

            for dig, times in counts:
                if dig == 0:
                    ztimes = times
                tot /= factorial(times)

            
            subby = (tot*(ztimes))//(n)
            tot -= subby
            #print(tot, counts)
            res += tot 

                

        #print(self.palset)
        return int(res)
        
29413