For a transformer decoder, how exactly are K, Q, and V for each decoding step?

Assume my input prompt is "today is a" (good day). 

At t= 0 (generation step 0):
K, Q, and V are the projections of the sequence ("today is a")
Then say the next token generated is "good".

At `t=1` (generation step 1):
Which one is true:
1. K, Q, and V are the projections of the sequence ("today is a good")
2. K, Q, are the projections of the sequence ("today is a"), and V is the projection of the sequence ("good")?