Adding key value pair in a nested map dynamically

Questions & Help Questions
1

I have this map:

               %{
                 "$include" => %{
                    "hospitals" => %{
                       "$include" => %{"rooms" => %{"beds" => %{}}},
                       "$order" => %{"id" => "$asc"}
                    },
                   "doctors" => %{
                       "$order" => %{"id" => "$desc"}                      
                    }
                 }
              }

There is any number of $include statements nested inside $include. so it should be dynamic. The output should be.

               %{
                 "$include" => %{
                    "hospitals" => %{
                       "$include" => %{"rooms" => %{"beds" => %{"binding" => "last"}, "binding" => "last"}},
                       "$order" => %{"id" => "$asc"},
                       "binding" => "first"
                    },
                   "doctors" => %{
                       "$order" => %{"id" => "$desc"},
                       "binding" => "first"
                    }
                 }
              }

All the outer maps should include binding => "first" and all nested include should contain "binding "=> "last".

Any help will be much appreciated.

Thanks