<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 string_to_base_26(self, s: str) -> list[int]:
        return [ord(c) - ord('a') for c in s]

    def search(self, nums: list[int], x: str, mod: int) -> list[int]:
        b = 26
        
        x_num = self.string_to_base_26(x)
        x_hash = 0
        x_size = len(x_num)
        
        for d in x_num:
            x_hash = (x_hash * b + d) % mod
        
        h = 0
        for d in nums[:x_size]:
            h = (h * b + d) % mod
        
        ids = []
        if h == x_hash:
            ids.append(0)

        P = b**x_size % mod

        for i in range(x_size, len(nums)):
            h = (h * b - nums[i - x_size] * P + nums[i]) % mod
            if h == x_hash:
                ids.append(i - x_size + 1)
        
        return ids
            

    def beautifulIndices(self, s: str, a: str, b: str, k: int) -> List[int]:
        mod = 10**9
        nums = self.string_to_base_26(s)
        idxs = self.search(nums, a, mod)
        jdxs = self.search(nums, b, mod)

        if not idxs or not jdxs:
            return []

        ans = []

        for i in idxs:
            j = bisect_left(jdxs, i)
            if (j > 0 or j == len(jdxs)) and abs(i - jdxs[j - 1]) <= k:
                ans.append(i)
            elif j < len(jdxs) and abs(i - jdxs[j]) <= k:
                ans.append(i)
        
        return ans
1353