Hail XOR

You are given a sequence $A_1, A_2, \ldots, A_N$ and you have to perform the following operation exactly $X$ times: - Choose two integers $i$ and $j$ such that $1 \le i \lt j \le N$. - Choose a non-negative integer $p$. - Change $A_i$ to $A_i \oplus 2^p$, and change $A_j$ to $A_j \oplus 2^p$, where $\oplus$ denotes [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR). Find the