$2)$ You designed and implemented the DC $($Dynamic C$),$ which is a new programming language with dynamic scoping. Consider the following code that can be run on both DC and C without any modification.

$```$

#include

int i $=0$; int j $=$

$5$; int k $=10$;

void h$($void$)\{$

printf $("$H$1$: $8$d

$",$ i$)$;

i$=$i$+$j$+$k; $//$ Program point $1$

printf $("$H$2$: $8$d

$",$ i$)$;

$\}$

void g$($void$)\{$

int k $=1000$;

printf $("$G$1$: $8$d

$",$i$)$;

i$=$i$+$j$+$k; $//$ Program point $2$

h$()$;

printf $("$G$2$: $\%$d

$",$ i$)$;

$\}$

void f$($void$)\{$

int j $=200$;

printf $("$F$1$: $8$d

$",$ i$)$;

i$=$i$+$j$+$k; $//$ Program point $3$

g$()$;

printf $("$F$2$: $\%$d

$",$ i$)$;

$\}$

void main $($void$)\{$

int i $=100$;

printf $("$M$1$: $8$d

$",$ i$)$;

f$()$;

printf $("$M$2$: $8$d

$",$ i$)$;

g$()$;

printf $("$M$3$: $8$d

$",$ i$)$;

h$()$; $//$ Program point $4$

printf $("$M$4$: $8$d

$",$ i$)$;

$\}$

$```$

a$)$What is the output, when the code is compiled with the $\backslash (\backslash$mathbf$\{$C$\}\backslash )$ compiler? Give the referencing environments at program points $\backslash (1,2,3\backslash )$ and $4.$

b$)$ What is the output, when the code is compiled with the new DC compiler? Give the referencing environments at program points $\backslash (1,2,3\backslash )$ and $4$ for each invocation of the corresponding function. Note that the referencing environment at each invocation might be totally different for the same program point.