Given volume of reagents find the chemical formula of nitrogen oxide $$\ce{NH3 + O2 -&gt; N_xO_y + H2O}$$

I know that there is $\pu{1 m^3}$ of both the nitrogen oxide and the ammonia and the volume of oxygen on the left side is $\pu{1.25 m^3}$.

I think that I should use the ideal gas equation. It is also obvious that there is only one atom of nitrogen in the oxide - I guess that there is also only one oxygen. 

Could anyone give me any hints?
As a hint, you could write balanced equations for oxidation to N2O, NO, NO2 and N2O5.  (Did I forget any nitrogen oxide?)  Then you can compare moles (or volumes, since we are talking gases) of starting materials and products.