Sorting pairs and singles to assign new ID

[SASPreK]

Hi!

I have the following data

data have;
   input id   dt test;
datalines;
ABCDE    20100429      T1
ABCDE    20100429      T2
ABCDE    20090908      T1
ABCDE    20090908      T2
ABCDE    20210823      T1
ABCUK    20191008      T1
ABCUK    20191008      T2
ABCUK    20230723      T1
 
;

 In this dataset based on the id, date, and test there are six records that are in 3 pairs and two records that are singles. I want to create a new variable doc_id
in which each unique pair will get a new id and and for singles the field will be blank. See below expected output.

  id                    dt                test     doc_id

ABCDE     20100429        T1       ABCDE-1
ABCDE     20100429        T2      ABCDE-1
ABCDE     20090908       T1      ABCDE-2
ABCDE     20090908       T2     ABCDE-2     
ABCDE     20210823         T1
ABCUK     20191008         T1      ABCUK-1
ABCUK     20191008         T2     ABCUK-1
ABCUK    20230723         T1

Thank you for your inputs!

[A_Kh]

data have;
   input id $  dt:yymmdd10. test $;
   format dt date11.;
datalines;
ABCDE    20100429      T1
ABCDE    20100429      T2
ABCDE    20090908      T1
ABCDE    20090908      T2
ABCDE    20210823      T1
ABCUK    20191008      T1
ABCUK    20191008      T2
ABCUK    20230723      T1
 
;

data want;
	set have ;
	by id dt notsorted;
	retain NEW_ID;
	if first.id and first.dt then NEW_ID=1;
	else if not first.id and first.dt then NEW_ID+1;
	if not (first.dt and last.dt) then doc_id= catx('-', id, new_id);
	drop new_id;
run;  

[Ksharp]

data have;
   input id $  dt :yymmdd10. test $;
   format dt yymmddn8.;
datalines;
ABCDE    20100429      T1
ABCDE    20100429      T2
ABCDE    20090908      T1
ABCDE    20090908      T2
ABCDE    20210823      T1
ABCUK    20191008      T1
ABCUK    20191008      T2
ABCUK    20230723      T1
;
data temp;
 set have;
 by id dt notsorted;
 if  first.id then n=0;
 if not (first.dt and last.dt) and first.dt then n+1;
run;
data want;
 set temp;
 by id dt notsorted;
 doc_id=catx('-',id,n);
 if first.dt and last.dt then call missing(doc_id);
run;