Problem

You are tasked with processing a large log file represented as a list of strings. Each string represents a log entry, and you need to identify the indices of entries that match specific error patterns. The patterns can include substrings and should be case-insensitive.

Input

• logs: List of strings, where each string is a log entry.
• patterns: List of strings representing the error patterns to search for.

Output

• A list of indices where the log entries match any of the specified patterns.

Examples

Example 1:

Input: logs = ["Error: Disk full", "Warning: High CPU usage", "ERROR: Disk not found"], patterns = ["error", "disk"]
Output: [0, 2]

Example 2:

Input: logs = ["Info: System running smoothly", "Warning: Low memory", "Critical: System crash"], patterns = ["critical", "warning"]
Output: [1, 2]

Constraints

• 1 <= len(logs) <= 10^5
• Each log entry is at most 100 characters long.
• Patterns are non-empty strings and can contain spaces.