<p>You are given a <strong>0-indexed</strong> string <code>s</code>, a string <code>a</code>, a string <code>b</code>, and an integer <code>k</code>.</p>

<p>An index <code>i</code> is <strong>beautiful</strong> if:</p>

<ul>
	<li><code>0 &lt;= i &lt;= s.length - a.length</code></li>
	<li><code>s[i..(i + a.length - 1)] == a</code></li>
	<li>There exists an index <code>j</code> such that:
	<ul>
		<li><code>0 &lt;= j &lt;= s.length - b.length</code></li>
		<li><code>s[j..(j + b.length - 1)] == b</code></li>
		<li><code>|j - i| &lt;= k</code></li>
	</ul>
	</li>
</ul>

<p>Return <em>the array that contains beautiful indices in <strong>sorted order from smallest to largest</strong></em>.</p>

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

<pre>
<strong>Input:</strong> s = &quot;isawsquirrelnearmysquirrelhouseohmy&quot;, a = &quot;my&quot;, b = &quot;squirrel&quot;, k = 15
<strong>Output:</strong> [16,33]
<strong>Explanation:</strong> There are 2 beautiful indices: [16,33].
- The index 16 is beautiful as s[16..17] == &quot;my&quot; and there exists an index 4 with s[4..11] == &quot;squirrel&quot; and |16 - 4| &lt;= 15.
- The index 33 is beautiful as s[33..34] == &quot;my&quot; and there exists an index 18 with s[18..25] == &quot;squirrel&quot; and |33 - 18| &lt;= 15.
Thus we return [16,33] as the result.
</pre>

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

<pre>
<strong>Input:</strong> s = &quot;abcd&quot;, a = &quot;a&quot;, b = &quot;a&quot;, k = 4
<strong>Output:</strong> [0]
<strong>Explanation:</strong> There is 1 beautiful index: [0].
- The index 0 is beautiful as s[0..0] == &quot;a&quot; and there exists an index 0 with s[0..0] == &quot;a&quot; and |0 - 0| &lt;= 4.
Thus we return [0] as the result.
</pre>

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

<ul>
	<li><code>1 &lt;= k &lt;= s.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= a.length, b.length &lt;= 10</code></li>
	<li><code>s</code>, <code>a</code>, and <code>b</code> contain only lowercase English letters.</li>
</ul>

class Solution:
    def beautifulIndices(self, s: str, a: str, b: str, k: int) -> List[int]:
        matches_for_a = self.find_indices_of_subset(s, a)
        print(matches_for_a)
        matches_for_b = self.find_indices_of_subset(s, b)
        print(matches_for_b)

        res = self.check_difference(matches_for_a, matches_for_b, k)
        print(res)
        return res
    
    def find_indices_of_subset(self, parent: str, child: str) -> List[int]:
        """
        ex/
        parent = isawsquirrelnearmysquirrelhouseohmy
        child = my
        output = [16, 33]
        ex/
        parent = isawsquirrelnearmysquirrelhouseohmy
        child = squirrel
        output = [4, 18]
        """
        indices = []
        start_index_of_subset = 0

        while True:
            start_index_of_subset = parent.find(child, start_index_of_subset)
            if start_index_of_subset == -1:
                break
            indices.append(start_index_of_subset)
            start_index_of_subset += 1
        
        return indices

    
    def check_difference(self, matches_a: List[str], matches_b: List[str], k: int) -> List[int]:
        """
        ex/
        matches_a = [16, 33]
        matches_b = [4, 18]
        k = 15
        -> Process:
            abs(16 - 4) = 12. 12 <= 15? YES
            abs(16 - 18) = 2. 2 <= 15? YES (technically didn't need to check this as already satisfied 16)
            abs(33 - 4) = 29. 29 <= 15? NO
            abs(33 - 18) = 15. 29 <= 15? YES
        """
        matches_a = sorted(matches_a)
        matches_b = sorted(matches_b)
        res = []
        for num_a in matches_a:
            for num_b in matches_b:
                if abs(num_a - num_b) <= k:
                    res.append(num_a)
                    break
        
        return res


        
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