How to update an mongo array whithin c++ vector

I have a question that official examples couldn’t help me out
I am trying to update a array inside of a single document by c++ vector. Here is an example test document:

  "_id" : "05469b3c-73ad-412e-9703-52567269e7aa",
  "quality" : "2",
  "author" : [ 
    "Kawamura T", 
    "Imamura CK", 
    "Kenmotsu H", 
    "Taira T", 
    "Omori S", 
    "Nakashima K", 
    "Wakuda K", 
    "Ono A", 
    "Naito T", 
    "Murakami H", 
    "Mushiroda T", 
    "Takahashi T", 
    "Tanigawara Y"

and I have a new author list writing in vector that want to replace the “author” array in mongodb,what is the exact synatx to do that like

collection.update_one(make_document(kvp("_id", oid)), 
    make_document(kvp("$set", make_document(kvp("quality", 6))))

after searching maybe it will be like:

vector<string> new_author_list;

for (int i = 0; i < new_author_list.size(); i++)
    string& single_new_auther = new_author_list[i];
    collection.update_one(make_document(kvp("_id", uuid)), 
        make_document(kvp("$set", make_document(
            kvp("author." + i, single_new_auther)

but I am not sure, because I can’t find any similar example in mongo-cxx-driver-rx.x.x/examples/mongocxx