Question 96
Let $k$ be a positive integer. Set $a_{1}=1$ and, for every $n \geq 1$, $a_{n+1}=k\left(a_{1}+\cdots+a_{n}\right)+1$ (so for example $a_{2}=k a_{1}+1$ and $a_{3}=k\left(a_{1}+a_{2}\right)+1$). What is the smallest value of $k$ such that $a_{2016}$ is a multiple of $3^{4031} \cdot 7^{4027}$?
(A) 1271
(B) 1322
(C) 1331
(D) 1702
(E) 2048
(A) 1271
(B) 1322
(C) 1331
(D) 1702
(E) 2048