return ID's of unique combinations

My data table has the following format

ID   Var1   Var2   Var3   ...
1_1  0      0      1      ...
1_2  1      1      0      ...
1_3  0      0      1      ...
...  ...    ...    ...    ...

I want to extract the ID's from unique combinations (Varcolumns). Getting the unique combinations is not the problem (plyr::count(), aggregate() etc), I want to extract the id variables contributing to these unique combinations.

The output should look somewhat like this

Var1   Var2   Var3   IDs
0      0      1      1_1, 1_3
1      1      0      1_2

where the IDs column is a vector/list of all the ID's contributing to a unique combination.

I tried an R package and dplyr pipelines, nothing worked so far.

Any suggestions or even R packages how to handle this task?

Thank you!