${\displaystyle \underset{i=1}{\overset{|\text{~}logn\text{~}|}{}}}{\displaystyle \underset{j=1}{\overset{4^i}{}}},{\displaystyle \underset{k=1}{\overset{4^j}{}}}\frac{(2^j+\sqrt[\phantom{2}]{k}{)}^{2}logk}{2^i(j{4}^j+klogk)klogjlogi}=(?)$

a$.$ None of the other choices.

b$.n^{3}logn$

c$.\frac{n^3}{lognloglogn}$

d$.\frac{n^8}{lognloglogn}$

e$.n^{8}loglogn$