Calculating the gas constant of saturated moist air

How to calculate the gas constant of saturated moist air at 16 degree Celsius and 1.013 bar?

I'm not sure where to go with this. I just know that the saturated vapor pressure from steam tables, at 16 degree Celsius is 0.018173 bar. Is this data even useful for calculating the gas constant?

$$R=\frac{N_A \, k_B}{M}$$ with specific gas constant $R$, Avogadro number $N_A$, Boltzmann constant $k_B$ and molar mass $M$.
For a mixture of ideal gases (remembering $pV = N k_B T$): $$x_i = \frac{N_i}{N} = \frac{p_i}{p}$$ with pressure $p$, volume $V$, number of molecules $N$, temperature $T$ and mole fraction $x$. Indices refer to individual species, non-indexed values are for the mixture: $p_{\mathrm{Water}}$ = water partial gas pressure, $p$ = total pressure. Remember that $V_i=V$ and $T_i=T$ for mixtures.
Finally (see Wikipedia), $$M =\sum_j \, x_j \, M_j$$
You have $p_{\mathrm{Water}}$ and $p$, which allows you to calculate $p_{\mathrm{Air}}$ (the difference), all $x_i$, then $M$ and finally $R$.