<p>You are given a string <code>s</code> and a positive integer <code>k</code>.</p>

<p>Let <code>vowels</code> and <code>consonants</code> be the number of vowels and consonants in a string.</p>

<p>A string is <strong>beautiful</strong> if:</p>

<ul>
	<li><code>vowels == consonants</code>.</li>
	<li><code>(vowels * consonants) % k == 0</code>, in other terms the multiplication of <code>vowels</code> and <code>consonants</code> is divisible by <code>k</code>.</li>
</ul>

<p>Return <em>the number of <strong>non-empty beautiful substrings</strong> in the given string</em> <code>s</code>.</p>

<p>A <strong>substring</strong> is a contiguous sequence of characters in a string.</p>

<p><strong>Vowel letters</strong> in English are <code>&#39;a&#39;</code>, <code>&#39;e&#39;</code>, <code>&#39;i&#39;</code>, <code>&#39;o&#39;</code>, and <code>&#39;u&#39;</code>.</p>

<p><strong>Consonant letters</strong> in English are every letter except vowels.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;baeyh&quot;, k = 2
<strong>Output:</strong> 2
<strong>Explanation:</strong> There are 2 beautiful substrings in the given string.
- Substring &quot;b<u>aeyh</u>&quot;, vowels = 2 ([&quot;a&quot;,e&quot;]), consonants = 2 ([&quot;y&quot;,&quot;h&quot;]).
You can see that string &quot;aeyh&quot; is beautiful as vowels == consonants and vowels * consonants % k == 0.
- Substring &quot;<u>baey</u>h&quot;, vowels = 2 ([&quot;a&quot;,e&quot;]), consonants = 2 ([&quot;b&quot;,&quot;y&quot;]). 
You can see that string &quot;baey&quot; is beautiful as vowels == consonants and vowels * consonants % k == 0.
It can be shown that there are only 2 beautiful substrings in the given string.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;abba&quot;, k = 1
<strong>Output:</strong> 3
<strong>Explanation:</strong> There are 3 beautiful substrings in the given string.
- Substring &quot;<u>ab</u>ba&quot;, vowels = 1 ([&quot;a&quot;]), consonants = 1 ([&quot;b&quot;]). 
- Substring &quot;ab<u>ba</u>&quot;, vowels = 1 ([&quot;a&quot;]), consonants = 1 ([&quot;b&quot;]).
- Substring &quot;<u>abba</u>&quot;, vowels = 2 ([&quot;a&quot;,&quot;a&quot;]), consonants = 2 ([&quot;b&quot;,&quot;b&quot;]).
It can be shown that there are only 3 beautiful substrings in the given string.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> s = &quot;bcdf&quot;, k = 1
<strong>Output:</strong> 0
<strong>Explanation:</strong> There are no beautiful substrings in the given string.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= s.length &lt;= 1000</code></li>
	<li><code>1 &lt;= k &lt;= 1000</code></li>
	<li><code>s</code> consists of only English lowercase letters.</li>
</ul>

class Solution:
    def beautifulSubstrings(self, s: str, k: int) -> int:
        satisfied_equal_pairs = {i for i in range(501) if (i * i) % k == 0}

        vowels_consonants_pairs = {(0, 0)}
        cur_num_vowels = cur_num_consonants = res = 0
        for c in s:
            if c in "ueoai": cur_num_vowels += 1
            else: cur_num_consonants += 1
            
            min_num = min(cur_num_vowels, cur_num_consonants, 500)
            for i in range(min_num + 1):
                if i in satisfied_equal_pairs and \
                    (cur_num_vowels - i, cur_num_consonants - i) in vowels_consonants_pairs:
                    res += 1
            vowels_consonants_pairs.add((cur_num_vowels, cur_num_consonants))
    
        return res
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