Fix bulk solver failing to fetch problems at higher indices

The LeetCode API caps results at 100 per request, but the original code
requested 5000 in a single query. Problems at index 0-49 worked by luck
(their IDs were in the first 100 results), but problems 50+ had IDs
outside that initial batch.

Fix: Implement proper pagination to fetch all ~3800 problems in batches
of 100, with a global cache for efficient lookups across bulk operations.

Author: jeremymanning