Find Beautiful Indices in the Given Array II

You are given a **0-indexed** string `s`, a string `a`, a string `b`, and an integer `k`. An index `i` is **beautiful** if: - `0 <= i <= s.length - a.length` - `s[i..(i + a.length - 1)] == a` - There exists an index `j` such that: - `0 <= j <= s.length - b.length` - `s[j..(j + b.length - 1)] == b` - `|j - i| <= k` Return _the array that contains beautiful indices in **sorted order from smallest to largest**_.   **Example 1:** **Input:** s = "isawsquirrelnearmysquirrelhouseohmy", a = "my", b = "squirrel", k = 15 **Output:** [16,33] **Explanation:** There are 2 beautiful indices: [16,33]. - The index 16 is beautiful as s[16..17] == "my" and there exists an index 4 with s[4..11] == "squirrel" and |16 - 4| <= 15. - The index 33 is beautiful as s[33..34] == "my" and there exists an index 18 with s[18..25] == "squirrel" and |33 - 18| <= 15. Thus we return [16,33] as the result. ``` **Example 2:** **Input:** s = "abcd", a = "a", b = "a", k = 4 **Output:** [0] **Explanation:** There is 1 beautiful index: [0]. - The index 0 is beautiful as s[0..0] == "a" and there exists an index 0 with s[0..0] == "a" and |0 - 0| <= 4. Thus we return [0] as the result. ```   **Constraints:** - `1 <= k <= s.length <= 5 * 105` - `1 <= a.length, b.length <= 5 * 105` - `s`, `a`, and `b` contain only lowercase English letters.