Batch inference requests under a capacity budget

Question

A serving path receives requests in order. Pack them greedily into batches that respect both a total-size capacity and a maximum request count, then report the batch count and batch sizes.

```python
def solve(raw: str) -> str: ...
```

- The first line has two integers: the batch capacity `C` and the maximum request count per batch `B`. The second line is the request count `n`, and the third line has `n` request sizes.
- Walk the requests in input order. Add the next request to the current batch when the total size stays within `C` and the count stays within `B`; otherwise close the batch and start a new one.
- Every request must be placed exactly once, in order; a request equal to `C` forms its own batch.
- Return `batches=<count>;sizes=<s1>,<s2>,...` with the batch totals in order. Do not append a trailing newline.