Objective

Given a string txt and a string pat, your task is to find all occurrences of pat and its k-tuples in txt, but with the following constraints:

1. Character Frequency Constraint: You can only use characters from pat that appear in txt at least as many times as they do in pat. If pat contains a character that is not present in txt or is present fewer times than required, that permutation should not be considered.
2. Maximum Length Constraint: You can only consider substrings of txt that are of a maximum length L. If the length of pat exceeds L, return an empty list.
3. Output Format: Return the starting indices of all valid substrings in txt that are permutations of pat.

Worked Example

Input:

txt = "BACDGABCDA"

pat = "ABCD"

L = 4

Output:

[0, 5, 6]

Explanation: The valid substrings that are k-tuples of pat and within the length constraint are "BACD" at index 0, "ABCD" at index 5, and "BCDA" at index 6.

Input:

txt = "AABBCDAAB"

pat = "AB"

L = 4

Explanation:

The function checks for all substrings of txt that can be formed using the characters in pat with repetition allowed, while also ensuring that the length of the substring does not exceed L.

The valid substrings of length up to L that can be formed from pat are:

"AB"

"BA"

The function finds the starting indices of these substrings in txt:

"AA" (indices 0 and 1) can form "AB" and "BA".

"AB" at index 5.

Thus, the output is [0, 1, 5], indicating the starting indices of the valid substrings.

This example demonstrates how to find occurrences of k-tuples (or bags) that are permutations with repetition, allowing for a more flexible approach to substring matching.

I/O format

Flexible; default I/O policies apply.