Given array is sorted. Let two pointers $i$ and $j$, both be pointing to the first element.
If the difference of elements $arr\left [ i \right ]$ and $arr\left [j \right ] > m$, increment $i$.
If the difference of elements $arr\left [ i \right ]$ and $arr\left [ j \right ]$ is $< m$, increment $j$.
Otherwise, we found the exact difference $m$ at indices $i$ and $j$.
This procedure will take $O$$\left ( p \right )$time but not $O$$\left ( \log p \right )$.
option $B$