A Berkeley clock master has a time of $1$:$20$:$05.$ Two slave systems, A and B$,$ synchronize with the master. Currently, A has a time of $1$:$20$:$02$ and B has a time of $1$:$20$:$14.$ After synchronizing, to what value does A set its clock?

A$)1$:$20$:$00$

B$)1$:$20$:$02$

C$)1$:$20$:$03$

D$)1$:$20$:$07$