When the rate of the reaction 2NO+O2=2NO2 was studied, the rate was found to double when the O2 concentration alone was doubled but to quadruple when the NO concentration alone was doubled. Which of the following mechanisms accounts for these observations?

Question

When the rate of the reaction 2NO+O2=2NO2 was studied, the rate was found to double when the O2 concentration alone was doubled but to quadruple when the NO concentration alone was doubled.  Which of the following mechanisms accounts for these observations?
a.) Step 1: NO + O2=NO3 (and its reverse)
Step 2 (slow): NO+NO3=NO2+NO2

b.) Step 1 (slow): NO+NO=N2O2
Step 2: O2+N2O2=N2O4
Step 3: N2O4=NO2+NO2

I thought that the rate law for the overall reaction was R=k[NO]^2[O2] but that doesn't match either of the slow reaction steps.  Thanks.