Let x_{0}, x_{1}, x_{2}, \cdots be a sequence of numbers, where each x_{k} is either 0 or 1 . For each positive integer n, define

S_{n}=\sum_{k=0}^{n-1} x_{k} 2^{k}

Suppose 7 S_{n} \equiv 1\left(\bmod 2^{n}\right) for all n \geq 1. What is the value of the sum

x_{2019}+2 x_{2020}+4 x_{2021}+8 x_{2022} ?

**Answer Choices**

A. 6

B. 7

C. 12

D. 14

E. 15