Divisi Staff with instrument name at the left

[Caio Barros]

I'm trying to write a divisi staff that appears at the middle of the system and I want to write the instrument name at the left of the beginning of the staff.
Is there a way to do that?

Example: I want to write "Cl. 1" a the left of the inserted staff in the code below:

\new Staff = "Clarinets" \relative a'' {
  \set Staff.instrumentName = "Cl. 1 & 2"
  <a d>4
  <<
    \new Staff \with { alignAboveContext = "Clarinets" }
    { \pitchedTrill g2. \startTrillSpan a s4 \stopTrillSpan }
    { \pitchedTrill a2.\startTrillSpan gis s4 \stopTrillSpan }
  >>
}

thanks!