Consider the following program fragment $($ no "backdoor" reference is allowed$)$:

program Main;

var x$,$ ct$,$ z : integer;

program P$1$;

var a$,$ ct : integer;

program P$2$;

var a$,$ b$,$ x : integer;

begin..end; $\{$P$2\}$

begin..end; $\{$P$1\}$

procedure P$3$;

var b$,$ y$,$ ct : integer;

procedure P$4$;

var a$,$ b : integer;

begin $...$ end; $\{$P$4\}$

begin $..$ end; $\{$P$3\}$

begin $..$ end; $\{$Main$\}$

Assuming static scoping, list all of the variables in the form procedure.variable, where procedure is the name of the procedure declaring the variable $($P$2.$a for variable a declared in procedure $2)$ that are visible in each body for P$1,$ P$2,$ P$3,$ P$4.$