I work on sql server 2012 i face issue i need to make select statment get Partid from last month until current month

based on last date exist per partid

and on same time if there are any gaps between dates then file it based on last date

so

first case if i found partid with last date 2022-01-08 then i will add 08-02-2022 and 08-03-2022 as partid 6070

second case if partid with date on month 7 and month 10 and no date per part id on month 8 and 9 then it must display this gap

according to last month as partid 1234 have gap

both cases must applied for all data based on partid

date used below on formate yyyy-mm-dd

create table Parts
 (
    
 PartId int,
 CreatedDate date
 )
 insert into Parts(PartId,CreatedDate)
 values
 (1234,'2021-07-03'),
 (1234,'2021-10-05'),
 (1234,'2021-11-05'),
 (5981,'2021-11-15'),
 (5981,'2021-12-03'),
 (6070,'2021-12-12'),
 (6070,'2022-01-08')

i need to make select statment display parts as expected result

green rows only for more clear that these parts must added

Expected result

PartId	CreatedDate
1234	2021-07-03
1234	2021-08-03
1234	2021-09-03
1234	2021-10-05
1234	2021-11-05
1234	2021-12-05
1234	2022-01-05
1234	2022-02-05
1234	2022-03-05
5981	2021-11-15
5981	2021-12-03
5981	2022-01-03
5981	2022-02-03
5981	2022-03-03
6070	2021-12-12
6070	2022-01-08
6070	2022-02-08
6070	2022-03-08

What I have tried:

what i try

with cte as (
      select partid, month(CreatedDate),
             dateadd(month, -1,
                     coalesce(lead(month(CreatedDate)) over (partition by partid order by month(CreatedDate)),
                              max(month(CreatedDate)) over ()
                             )
                    ) as end_month
      from Parts
      union all
      select partid, dateadd(month, 1, month(CreatedDate)) as monthes, end_month
      from cte
      where monthes < end_month
     )
select *
from cte
order by partid, month;