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
/**
 * @param {number} n
 * @param {number} k
 * @return {number}
 */
var countGoodIntegers = function (n, k) {
    const fac = factorial(n);
    let ans = 0;
    const vis = new Set();
    const base = Math.pow(10, Math.floor((n - 1) / 2));

    for (let i = base; i < base * 10; i++) {
        let s = String(i);
        const rev = reverseString(s);
        if (n % 2 === 1) {
            s += rev.substring(1);
        } else {
            s += rev;
        }

        if (parseInt(s, 10) % k !== 0) {
            continue;
        }

        const bs = Array.from(s).sort();
        const t = bs.join('');

        if (vis.has(t)) {
            continue;
        }

        vis.add(t);

        const cnt = Array(10).fill(0);
        for (const c of t) {
            cnt[parseInt(c, 10)]++;
        }

        let res = (n - cnt[0]) * fac[n - 1];
        for (const x of cnt) {
            res /= fac[x];
        }
        ans += res;
    }

    return ans;
};

function factorial(n) {
    const fac = Array(n + 1).fill(1);
    for (let i = 1; i <= n; i++) {
        fac[i] = fac[i - 1] * i;
    }
    return fac;
}

function reverseString(s) {
    return s.split('').reverse().join('');
}
