$3.$ We are performing a $16-$bit subtraction of Z $=$ X $-$ Y$,$ where X $=4587.$ Suppose some pieces of information are known on the $16-$bit fast adder$$s top$-$level CLA$74182$ circuit, as annotated by the red numbers $($P$1=1,$ C$2=0,$ C$3=1,$ P$4=0,$ and C$4=1).$

a$)$Please derive the possible values of Y$,$ you should provide evidence for your answer.

b$)$Please give the possible results of Z$,$ and whether overflow happens by using the signals in the circuit for your answer. I need all the possibilities of Y$,$ not just the explanation of Y$1$Y$2,$ and why Y$1$Y$2$ can be judged through P and G$.$ Is there any specific expression relationship?