S$1,$ AS$2,$ and AS$3$ are ISPs, peering with each other at the links between routers J$-$K$,$ N$-$A$,$ and D$-$G$.$

$$ AS$6$ is a customer of AS$1$ and AS$3.$ Two more customer networks are shown.

$$ All routers are shown. All links between routers are shown. All networks are running OSPF as their IGP, and all link costs are equal.

$$ All providers are running I$-$BGP$.$

$$ The prefix for AS$6$ is $12\mathrm{.}2\mathrm{.}0\mathrm{.}0/16.$ The prefix for AS$65432$ is $135\mathrm{.}207\mathrm{.}16\mathrm{.}0/20.$ The prefix for the nameless customer containing router S and host d is $192\mathrm{.}20\mathrm{.}225\mathrm{.}0/24.$

$$ AS$1,$ AS$2,$ and AS$3$ number their routers out of $1\mathrm{.}0\mathrm{.}0\mathrm{.}0/8,2\mathrm{.}0\mathrm{.}0\mathrm{.}0/8,$ and $3\mathrm{.}0\mathrm{.}0\mathrm{.}0/8,$ respectively.

DO not make any unnecessary assumption. If you have to make any assumptions they have to be reasonable and state them very clearly.

$1.[2$ points$]$ Suppose that AS$6$ announces its entire prefix out of both X and Y$,$ and that it receives full BGP tables from its providers. What is the path from a to b$?$ From a to c$?$ From a to d$?$ From c to a$?$ From d to a$?$