Verify each finding against the current code and only fix it if needed.

Inline comments:
In `@tensorrt_llm/_torch/auto_deploy/custom_ops/mla/torch_backend_mla.py`:
- Line 325: The custom op registration for
"auto_deploy::torch_cached_mla_with_cache" currently hides side effects by using
mutates_args=(); update the decorator to declare the cache as mutated (e.g.
mutates_args=("mla_cache",)) so PyTorch's export/functionalization sees the
write; make the change on the `@torch.library.custom_op` line for the op
registered in torch_backend_mla.py (the function used by _update_mla_cache and
_torch_mla_generate_with_absorption modifies mla_cache), and ensure the op
signature/argument name matches the declared "mla_cache" identifier.

In `@tensorrt_llm/_torch/auto_deploy/custom_ops/mla/triton_mla.py`:
- Line 568: The code currently uses floor-division of num_heads by head_block
(e.g., computing num_head_blocks = num_heads // head_block) which drops tail
heads and leaves weighted_kv/out uninitialized; change these launches to use
ceil-division (num_head_blocks = (num_heads + head_block - 1) // head_block) and
add an in-kernel guard that checks computed head index < num_heads before
writing (so kernels skip work for masked tail lanes), or alternatively enforce
head_block divisibility by num_heads; update every occurrence that launches on
head_block (e.g., where head_block, num_heads, weighted_kv, out are used) to use
the ceil division and add the head-index bound check in the kernel entry to
ensure no heads are lost.
- Line 869: The custom op decorator for
auto_deploy::triton_cached_mla_with_cache incorrectly marks the op as pure;
update the `@torch.library.custom_op` on the function implementing
triton_cached_mla_with_cache to declare that mla_cache is mutated (e.g., change
mutates_args=() to include "mla_cache"), because helper functions
_triton_mla_decode and _triton_mla_prefill perform indexed assignments into
mla_cache and the op must be treated as mutating that argument.
- Around line 804-806: The current code forces a device-to-host sync by calling
seq_lengths.sum().item() (total_tokens) inside _triton_mla_prefill; instead,
change _triton_mla_prefill signature to accept an int num_prefill_tokens and
remove the seq_lengths.sum().item() call (and any use of total_tokens computed
from .item()), compute num_prefill_tokens at the wrapper call site using
BatchInfo.get_absorbed_info() and pass that int into _triton_mla_prefill; update
all call sites (the wrapper that currently prepares seq_lengths/seq_start_l
before calling _triton_mla_prefill) to pass the new num_prefill_tokens parameter
so no device-to-host sync occurs inside seq_lengths/seq_start_l handling.

---

Outside diff comments:
In `@tensorrt_llm/_torch/auto_deploy/custom_ops/mla/__init__.py`:
- Around line 1-17: Add the required NVIDIA SPDX copyright/license header at the
top of this module (above the module docstring) including the appropriate year
of the latest meaningful modification and the SPDX identifier; ensure it follows
the project's standard header format and appears before any imports or the
docstring so files like this one that export TorchBackendMLAAttention,
FlashInferMLAAttention, TritonMLAAttention, torch_mla,
torch_backend_mla_with_cache, flashinfer_mla_with_cache, and
triton_cached_mla_with_cache include the mandated NVIDIA header.

In `@tensorrt_llm/_torch/auto_deploy/custom_ops/mla/torch_backend_mla.py`:
- Around line 1-18: Add the required NVIDIA SPDX copyright header to the top of
the modified Python module (torch_backend_mla.py) before the module docstring;
include the appropriate SPDX identifier and the year of latest modification and
the NVIDIA copyright line consistent with project policy. Ensure the header
appears above the existing docstring so tools and legal scans pick it up, and
keep the rest of the file (including symbols torch_cached_mla_with_cache and
TorchBackendMLAAttention) unchanged.