Note that in analysis of algorithms, time complexity is typically measured in terms of the size of the input and not the input values. If n is a single number, then its binary string representation can be represented using approximately m bits $($the size of the input$),$ where m $=$ log$\_2($ n$).$ Therefore, the maximum value that can be expressed in m bits is n $=$ O$($exp$($ m$)).$ In terms of m$,$ what is the closest$-$fit worst$-$case time complexity of following algorithm?

f$($n$)\{$

if $($n $<2)$

return $1$

else

return f$($ n $-1)+$ n

Group of answer choices

a$.$

O$($ m$).$

b$.$

O$($log$($ m$)).$

c$.$

O$($exp$($ m$)).$

d$.$

None of the above.