Trie Autocomplete for Prefix Search

Problem

Implement a prefix tree (Trie) that stores lowercase menu items or command strings and supports real-time autocomplete. Design a function that first inserts all words from a list, then returns up to k lexicographically sorted suggestions that start with a given prefix. The function should return an empty list if no stored word matches the prefix.

Constraints

• 1 <= len(words) <= 10^4
• 1 <= len(words[i]) <= 30
• 0 <= len(prefix) <= 30
• 1 <= k <= 100
• All strings contain only lowercase English letters
• Words in words are unique