Could Dinosaurs have posterior and anterior airsacs like birds?

I just learnt that birds have posterior and anterior airsacs in their bodies that allow for better oxygen intake. This allows them to take in more oxygen than reptiles and mammals enabling them to be able to fly long distances.
Could that mean Dinosaurs also had them? or atleast the ones that survived the toxic atmosphere that came after meteor impact and evolved into birds?
I can imagine a large number of smaller sized theropods having them enabling them to survive the extinction and evolve into birds. But this is just a random person's opinion without supporting evidence.