fulfilling qadhaa salaats

I am making up my qada salat. i have already made up many of my qada salat already. But i wanted to know whether the intention that i had was correct for the qada salar made up.  For instance if i was making up qada of fajar i would intend that this is the "first" fajar salat qada and i would make the exact same niyyat for the following qadas of fajar. i have done this so far for all the qada salats i have made up so far. also somethimes i would just intend that this is qada of salah "x" and thats it. is this correct?