Prime Xor

For $3$ **distinct prime** integers $A, B,$ and $C$ $(1 \lt A,B,C \lt 2^{30})$, we define positive integers $X, Y,$ and $Z$ as: $X = A\oplus B, Y = B\oplus C,$ and $Z = C\oplus A$, where $\oplus $ denotes the [bitwise XOR](https://en.wikipedia.org/wiki/Bitwise_operation#XOR) operation. Given only **two** integers $X$ and $Y$ and the fact that **at least one** integer amongst $X, Y,$ and $Z$ is