 Truncated lognormal moment

If $\log S=m+sZ$ with a standard normal $Z$, then $\mathbb{E}[S^p{1}_{\{S>K\}}]=e^{pm+p^2{s}^2/2}\Phi ((m+p{s}^2-\log K)/s)$. Completing the square proves the formula for every real $p$, including the inverse-price moment $p=-1$.