$```$

statement $->$ assignment $|$ subr$\_$call

assignment $->$ id:$=$expr

subr$\_$call $->$ id $($arg$\_$list$)$

expr $->$ primary expr$\_$tail

primary $->$ id $|$ subr$\_$call $|($expr$)$

op $->+|-|*|/$

arg$\_$list $->$ expr arg$\_$tail

arg$\_$tail $->,$ arg$\_$list $|$

a$)$ Construct a parse tree for the input string "bar $($a$,$b$)".(10$ points$)$

b$)$ With the grammar above is it possible to create a parse tree for the input string "foo $($a$,$ b$,$ d$)"?$ If yes, construct a parse tree for the input string foo $($ a$,$ b$,$ d$).$ If no$,$ explain the reason. $(10$ points$)$

c$)$ Provide the rightmost derivation of "bar $($a$,$ b$)".(10$ points$)$

d$)$ Explain how this grammar will not work for LL $(1)?(5$ points$)$

e$)$ Modify the grammar so that it is LL $(1).(10$ points$)$