AMC 10A 2020 Problem 21

There exists a unique strictly increasing sequence of nonnegative integers a_{1}<a_{2}<\cdots<a_{k} such that

\dfrac{2^{289}+1}{2^{17}+1}=2^{a_{1}}+2^{a_{2}}+\cdots+2^{a_{k}}

What is k ?

Answer Choices
A. 117
B. 136
C. 137
D. 273
E. 306