mongodb c-api中的$exists查询

我试图在C中实现以下mongodb查询

db.test.find（{“timestamp”：{“$exists”：true}）

我以为会是这样

bson query, existspart;
mongo_cursor cursor;
int i;

bson_init(&existspart);
bson_append_string ( &existspart, "$exists", "false" );
bson_finish(&existspart);
bson_init(&query);
bson_append_bson ( &query, "timestamp", &existspart );
bson_finish(&query);    

mongo_cursor_init(&cursor, conn, "mydb.test");
mongo_cursor_set_query(&cursor, &query );
while( mongo_cursor_next( &cursor ) == MONGO_OK )
{
    // blabla
} 

但它不起作用。我做错了什么？
替换

bson_append_string ( &existspart, "$exists", "false" );

与

或

如果您不希望该字段存在
我使用了稍微不同的语法：

bson_t* existspart = BCON_NEW("$exists", BCON_BOOL(true));
bson_t *query = bson_new();
BSON_APPEND_DOCUMENT(query, "timestamp", existspart);

mongoc_cursor_t* cursor = MongoInterface::Instance().Find("db_name", query);

const bson_t *doc;
while (mongoc_cursor_next (cursor, &doc))
{
  // Do stuff...
}

bson_destroy (existspart);
bson_destroy (query);

bson_append_bool ( &existspart, "$exists", 0 );

bson_t* existspart = BCON_NEW("$exists", BCON_BOOL(true));
bson_t *query = bson_new();
BSON_APPEND_DOCUMENT(query, "timestamp", existspart);

mongoc_cursor_t* cursor = MongoInterface::Instance().Find("db_name", query);

const bson_t *doc;
while (mongoc_cursor_next (cursor, &doc))
{
  // Do stuff...
}

bson_destroy (existspart);
bson_destroy (query);