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.