  In this work, we show that the difference of a Hauptmodul for a genus zero
group $\Gamma_{0}(N)$ as a Hilbert modular function on $Y_{0}(N)\times
Y_{0}(N)$ is a Borcherds lift of type $(2,2)$. As applications, we derive
Monster denominator formula like product expansions for these Hilbert modular
functions and certain Gross-Zagier type CM value formulas.
