Training examples must be packed into token-limited batches without changing their order. Implement batching so oversized examples and exact capacity boundaries follow the agreed policy.
Build the implementation in Rust under /app, with /app/run.sh as its entry point. Read one JSON request from standard input and write one JSON result to standard output. Input has positive integer budget and lengths, a list of positive integer token counts no greater than budget. Greedily append the next example to the current batch when it fits, otherwise start a new batch. Return batches of original zero-based example indices and unused tokens per batch. Reject invalid or oversized lengths.
Reject inputs that violate an explicit validation rule with exit status 2, no standard output, and {"error":"invalid_input"} on standard error. For valid input, exit with status 0. Keep the implementation reusable for new inputs; it must work offline and must not depend on the example data being the only data it receives.
Repair or replace the unfinished /app/run.sh and add source files under /app. Malformed JSON must use the same invalid-input response. Do not read /tests or /oracle from the application.