Hello, I have a question about taking mod of 2 separate numbers. Specifically, let's say that we want to calculate a value on $$$mod = 998244353$$$ as usual.

Additionally, we precalculate the powers of 2 based on that mod (say up to $$$2^{1000}$$$). And let's say that we have a number $$$k$$$ based on $$$mod$$$.

My question is, is it possible to calculate $$$k$$$ % $$$2^{1000} \equiv mod$$$ in our modular base? If so, how?

Thanks in advance!