How to clear the dataframe by removing false rows in R

I have many csv files with dataframes looking like these.
 
Dummy Data:
df1 <- structure(list(Date = c("24/06/2002", "24/06/2002", "25/06/2002", 
                               "02/07/2002","24/07/2002", "08/07/2002",
                               "08/07/2002", "15/07/2002", "17/07/2002", 
                               "22/07/2002", "22/07/2002", "28/07/2002", "29/07/2002"), 
                      payment = c(200,   1000, 1000, 
                                  -1000,-1000, 1200,
                                  -1200, 1200, 1200,
                                  200, 56700, -56700, -200), 
                      Code = c("ABC", "M567", "M567", "M567", 
                               "M567","M567", "M567", 
                                "M567", "M567", "M300", 
                               "M678", "M678", "ABC"), 
                      ID = c(NA, "98","98","M11",
                             NA,"K999", 
                             "K999", "111", "111", "11",
                             "12345", NA, NA)), row.names = c(NA, -13L), class = "data.frame")

Some of the rows are just return of payment (falsely entered):

        Date payment Code    ID
1  24/06/2002     200  ABC  <NA>
2  24/06/2002    1000 M567    98
3  25/06/2002    1000 M567    98
4  02/07/2002   -1000 M567   M11
5  24/07/2002   -1000 M567  <NA>
6  08/07/2002    1200 M567  K999
7  08/07/2002   -1200 M567  K999
8  15/07/2002    1200 M567   111
9  17/07/2002    1200 M567   111
10 22/07/2002     200 M300    11
11 22/07/2002   56700 M678 12345
12 28/07/2002  -56700 M678  <NA>
13 29/07/2002    -200  ABC  <NA>

I want to delete the rows that has a same +ve and -ve payment by taking Code and ID into consideration. 
i.e., 

 - if the code and ID column matches and the payment is cancelling out then delete those two columns 
 - if ID is present for +ve payment and absent for -ve payment viseversa then only take Code for grouping
- If ID is absent for both +ve and -ve then only take Code column for grouping

So, the resultant dataframe for all the csv files should be like these:

  Date       payment Code  ID   
  <chr>        <dbl> <chr> <chr>
1 22/07/2002     200 M300  11   
2 15/07/2002    1200 M567  111  
3 17/07/2002    1200 M567  111  
4 25/06/2002    1000 M567  98   
5 02/07/2002   -1000 M567  M11        
       
      
Can anyone help me with this?<pre>

#But this code doesnt work for cases with NAs
library(dplyr)
library(data.table)
library(tidyr)
df1 %>% 
  group_by(Code) %>%
  fill(ID, .direction = "downup") %>%
  ungroup %>% 
  mutate(absPayment = abs(payment)) %>% 
  arrange(ID, Code, absPayment) %>%
  group_by(Code, ID, absPayment) %>%
  mutate(grp = rowid(sign(payment))) %>% 
  group_by(grp, .add = TRUE) %>%
  filter(n() == 1) %>%
  ungroup %>% 
  select(-grp, -absPayment)