Speed up sampling from truncated distribution

Questions
,
1

I am struggling trying to speed up a code to generate stochastic vectors, sampled from a truncated Dirichlet distribution. This is a small example:

Bmax = 0.05;
nvar = 100;
niter = 500;
p = 0.10;
smax = 7.;

b = ConstantArray[{0., Bmax}, nvar];

s = Table[If[1 <= i <= p nvar, smax, 1.], {i, 1, nvar + 1}];

RandomVariate[TruncatedDistribution[b, DirichletDistribution[s]], 
niter] // AbsoluteTiming // First

In my laptop, it takes around 2 s to generate that matrix with probability vectors. Is there any way I can speed up the code? I am interested in higher smax values, and I have noticed that the computation time increases very fast, which makes my application unfeasible.

Thanks in advance for any help!