$"$As shown in the figure below, m $=0\mathrm{.}005$ kg of air is contained in an adiabatic piston$-$cylinder apparatus that rests on a flat surface. The piston, which is massless, is attached to a spring with spring constant k $=36,415$ N$/$m and a free length $$L$0=0\mathrm{.}068$ m$.$ Initially the piston is held in place by a pin with the air in an unknown initial state. For this initial condition, the length of the spring is L$1=0\mathrm{.}1$ m$.$ The pin is removed and the system comes to a new equilibrium state for which the spring has a new length L$2=0\mathrm{.}029$ m and the air has a volume of V$2=0\mathrm{.}005$ m$3.$ The piston has an area A $=0\mathrm{.}003$ m$2.$ The atmosphere acting on the piston has a pressure of Patm $=105$ Pa$.$ The air can be modelled as an ideal gas with cv $=716$ J$/$kgK and R $=287$ J$/$kgK$.$

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Find the pressure of the air inside the piston$-$cylinder apparatus in state $2$ in units of Pa$.$ Provide the answer as a whole number $($zero decimal places$)."$