\[p(a,b)=\left\lfloor\tfrac{1}{2}\left(\left\lceil-b\right\rceil-\left\lceil-a%
\right\rceil+1\right)\right\rfloor-\left\lfloor\tfrac{1}{2}\left(\left\lceil-b%
\right\rceil-\left\lceil-a\right\rceil\right)\right\rfloor,\]