<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;= 5 * 10<sup>5</sup></code></li>
	<li><code>1 &lt;= a.length, b.length &lt;= 5 * 10<sup>5</sup></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]:
        valida = []
        validb = []
        ans = []
        lpsa = [0] * len(a)
        lpsb = [0] * len(b)
        j = 0
        i = 1
        while i < len(a):
            if a[i] == a[j]:
                j += 1
                lpsa[i] = j
                i += 1
                
            else:
                if j != 0:
                    j = lpsa[j - 1]
                else:
                    lpsa[i] = 0
                    i += 1

        j = 0
        i = 1
        while i < len(b):
            if b[i] == b[j]:
                j += 1
                lpsb[i] = j
                i += 1
                
            else:
                if j != 0:
                    j = lpsb[j - 1]
                else:
                    i += 1
 
        i = 0 
        j = 0
        while len(s) - i >= (len(a) - j):
            if a[j] == s[i]:
                j += 1
                i += 1
            
            if j == len(a):
                valida.append(i - j)  
                j = lpsa[j - 1]
            elif i < len(s):
                if a[j] != s[i]:
                    if j != 0:    
                        j = lpsa[j - 1]
                    else:
                        i += 1
        i = 0
        j = 0
        while len(s) - i >= len(b) - j:
            if b[j] == s[i]:
                j += 1
                i += 1
            
            if j == len(b):
                validb.append(i - j )   
                j = lpsb[j - 1]
            else:
                if b[j] != s[i]:
                    if j != 0:     
                        j = lpsb[j - 1]
                    else:     
                        i += 1

        
        print(valida, validb)
        while valida and validb:
            if abs(valida[-1] - validb[-1]) <= k:
                ans.append(valida[-1])
                valida.pop()
            
            elif  validb[-1] < valida[-1]:
                valida.pop()
                continue
                      
            elif validb[-1] > valida[-1]:
                while abs(valida[-1] - validb[-1]) > k and validb[-1] > valida[-1]:
                    validb.pop()
                    if not validb or not valida:
                        break
        
        return ans[::-1]
1074