Given two numbers X and Y $=$ y$\_(3)*10^(3)+$ y$\_(2)*10^(2)+$ y$\_(1)*10+$ y$\_(0),$ the product P $=$ y$\_(0)*$ X can be expressed as P $=$ y$\_(0)*$ X $*10^(0)+$ y$\_(1)*$ X $*10^(1)+$ y$\_(2)*$ X $*10^(2)+$ y$\_(3)*$ X$*10^(3).$

Which of the following algorithms compute P$?$ Mark all that apply.

a$.$

A ; B X;

for i in $0$ to $3$ loop

A A $+$ y$($i$)*$B;

B B$*10$;

end loop;

P A;

b$.$

P ; A X;

for i in $0$ to $2$ loop

P P $+$ y$($i$)*$A;

A A$*10$;

end loop;

P P $+$ y$(3)*$A;

c$.$

A X;

for i in $0$ to $2$ loop

P P $+$ y$($i$)*$A;

A A$*10$;

end loop;

P P $+$ y$(3)*$A;