The XOR Machine

You are given $4$ integers $X, L, R, $ and $M$. Consider the sequence of integers $A$ of length $R-L+1$, defined by $$ A_i = (X \oplus (L + i - 1)) \bmod M $$ where where $\oplus$ is the [Bitwise xor operator](https://en.wikipedia.org/wiki/Exclusive_or). That is, the $i$-th element of the sequence is obtained by taking the result of the bitwise XOR of $X$ and $(L + i - 1)$, and computing its