<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]:
        '''
        input:
         - s = 0-indexed string
         - a = string
         - b = string
         - k = integer

        return:
         - sorted array of all the beautilful indices

        beautiful index:
        -  0 <= i <= s.length - a.length -> index that can contain all of A in S 
        -  s[i....len(a)] == a -> substring from index i:len(a) is equal to a

        if this candidate exist 
        -  0 <= i <= s.length - b.length -> index that can contain all of B in S 
        -  s[i....len(b)] == b -> substring from index i:len(b) is equal to a
        - |j - i| <=k
        '''
        S = len(s)
        A = len(a)
        B = len(b)
        a_candidates = []
        for i in range(S - A + 1):
            if s[i:i + A] == a:
                a_candidates.append(i)
        b_candidates = []

        for i in range(S - B + 1):
            if s[i:i + B] == b:
                b_candidates.append(i)
        print(a_candidates, b_candidates)
        ans = []
        # for i in a_candidates:
        #     for j in b_candidates:
        #         if abs(j - i) <= k:
        #             ans.append(i)
        #             break
                
        i_ptr, j_ptr = 0, 0

        while i_ptr < len(a_candidates) and j_ptr < len(b_candidates):
            i, j = a_candidates[i_ptr], b_candidates[j_ptr]

            if abs(j - i) <= k:
                ans.append(i)
                i_ptr += 1
            elif j < i - k:
                j_ptr += 1
            else:
                i_ptr += 1

        return ans


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