Write a function$($s$)$ that generates $$ decay events of $+->++$ that are uniformly distributed over the allowed phasespace. The parameter $$ should be an argument of your function. Plot these events on a Dalitz plot for $=100000$ using a hist$2$d with $300$x$300$ bins.

"Allowed phasespace" here refers to the kinematically allowed region of the Dalitz plot, ie$.$ the area shown in the example Dalitz plots above.

Use the same units $($ GeV$2/4)$ and axes as in the example Dalitz plot on the left. To ease communication and make the code clearer we will use $->$ notation for the decay such that you will be working with the variables:

m$2$ab $-$ the invariant mass squared of the $+$ system

m$2$bc $-$ the invariant mass squared of the $+$ system

md$,$ ma$,$ mb$,$ mc $-$ the masses of the decaying $$ meson and the $3$ decay products respectively

The masses you should use are

m$\_$dmeson$=1\mathrm{.}97$

m$\_$kaon$=0\mathrm{.}498$

m$\_$pion$=0\mathrm{.}135$

Hint: Use the accept$-$reject Monte Carlo method with NumPy functions. You only need to generate m$2$ab and m$2$bc values for the events. The range of m$2$bc values kinematically allowed given a m$2$ab value can be found in eqn $49\mathrm{.}23$a and $49\mathrm{.}23$b of the PDG review $($note that the PDG uses $+->1+2+3$ notation$)$