mongo: update $push failed with "Resulting document after update is larger than 16777216" - mongodb

Question

I want to extend an large array using the update(.. $push ..) operation.
Here are the details:
I have a large collection 'A' with many fields. Amongst the fields, I want to extract the values of the 'F' field, and transfer them into one large array stored inside one single field of a document in collection 'B'.
I split the process into steps (to limit the memory used)
Here is the python program:
...
steps = 1000 # number of steps
step = 10000 # each step will handle this number of documents
start = 0
for j in range(steps):
print('step:', j, 'start:', start)
project = {'$project': {'_id':0, 'F':1} }
skip = {'$skip': start}
limit = {'$limit': step}
cursor = A.aggregate( [ skip, limit, project ], allowDiskUse=True )
a = []
for i, o in enumerate(cursor):
value = o['F']
a.append(value)
print('len:', len(a))
B.update( {'_id': 1}, { '$push': {'v' : { '$each': a } } } )
start += step
Here is the oupput of this program:
step: 0 start: 0
step: 1 start: 100000
step: 2 start: 200000
step: 3 start: 300000
step: 4 start: 400000
step: 5 start: 500000
step: 6 start: 600000
step: 7 start: 700000
step: 8 start: 800000
step: 9 start: 900000
step: 10 start: 1000000
Traceback (most recent call last):
File "u_psfFlux.py", line 109, in <module>
lsst[k].update( {'_id': 1}, { '$push': {'v' : { '$each': a } } } )
File "/home/ubuntu/.local/lib/python3.5/site-packages/pymongo/collection.py", line 2503, in update
collation=collation)
File "/home/ubuntu/.local/lib/python3.5/site-packages/pymongo/collection.py", line 754, in _update
_check_write_command_response([(0, result)])
File "/home/ubuntu/.local/lib/python3.5/site-packages/pymongo/helpers.py", line 315, in _check_write_command_response
raise WriteError(error.get("errmsg"), error.get("code"), error)
pymongo.errors.WriteError: Resulting document after update is larger than 16777216
Apparently the $push operation has to fetch the complete array !!! (my expectation was that this operation would always need the same amount of memory since we always append the same amount of values to the array)
In short, I don't understand why the update/$push operation fails with error...
Or... is there a way to avoid this unneeded buffering ?
Thanks for your suggestion
Christian