$($a$)$ Fill out the following forwarding table that has five entries, uses longest prefix matching, and forwards packets to the correct link interfaces. You need to fill out three parts, $(1),(2),$ and $(3),$ with simple binary number $($e$.$g$.,11100101)$ consisting of $1-32$ binary digits. Do not insert any space character $($or tab character in the middle of your answer$)$ other than $0$ or $1.(15$ points$)$

$$

Prefix Match$$ Link Interface

$11100000000$

$(1)1$

$(2)2$

$(3)3$

$$otherwise$3$

$$

$$

$$

$($b$)$ Describe how your forwarding table determines the appropriate link interface for datagrams with destination addresses: $(15$ points$)$

$(1)11001000100100010101000101010101$

$(2)11100001010000001100001100111100$

$(3)11100001100000000001000101110111$

Enter the interface number in your answers.