What does it mean to say $x_{1} mod -x_{2}$ or $-x_{1} mod x_{2}$ when $x > 0$

Question

I understand that $x_{1} \ mod \ x_{2} : x > 0$ is the remainder after dividing $x_{1}$ by $x_{2}$ ex: $5 \ mod \ 256 = 5$
but what does it mean to say $-x_{1} \ mod \ x_{2} : x > 0$ or $-5 \ mod \ 256$, I thought that it will be $-5$ but it's $251$, also the other way $x_{1} \ mod \ -x_{2} : x > 0$ or $5 \ mod \ -256$.