Since $0 \leq k_i < n$, as long as $i$ is not too large, we will have $0 \leq k_i + 2i+1 < 2n$. Therefore you can compute the modulo by checking whether $k_i+2i+1 \geq n$, and if so, subtracting $n$.
This works as long as $(n-1) + (2i+1) < 2n$, that is, as long as $i < n/2$. Usually $n$ is very large, and so we are never going to perform $n/2$ ...
(Can't leave a comment, unfortunately.)
I'm having the same issue. Here's the diagram (sorry, it's messy):
I've also found this on the web:
The algorithm to subtract two binary numbers using 2’s complement is
explained as following below −
Take 2’s complement of the subtrahend
Add with minuend
If the result of above addition has carry bit 1, then it is ...