Find the Count of Good Integers
<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>
Hash Table; Math; Combinatorics; Enumeration
func factorial(n int) []int64 {
	fac := make([]int64, n+1)
	fac[0] = 1
	for i := 1; i <= n; i++ {
		fac[i] = fac[i-1] * int64(i)
	}
	return fac
}

func countGoodIntegers(n int, k int) (ans int64) {
	fac := factorial(n)
	vis := make(map[string]bool)
	base := int(math.Pow(10, float64((n-1)/2)))

	for i := base; i < base*10; i++ {
		s := strconv.Itoa(i)
		rev := reverseString(s)
		s += rev[n%2:]
		num, _ := strconv.ParseInt(s, 10, 64)
		if num%int64(k) != 0 {
			continue
		}
		bs := []byte(s)
		slices.Sort(bs)
		t := string(bs)

		if vis[t] {
			continue
		}
		vis[t] = true
		cnt := make([]int, 10)
		for _, c := range t {
			cnt[c-'0']++
		}
		res := (int64(n) - int64(cnt[0])) * fac[n-1]
		for _, x := range cnt {
			res /= fac[x]
		}
		ans += res
	}

	return
}

func reverseString(s string) string {
	t := []byte(s)
	for i, j := 0, len(t)-1; i < j; i, j = i+1, j-1 {
		t[i], t[j] = t[j], t[i]
	}
	return string(t)
}
