I'm looking for a model satisfying the inequality described in the title. Recall that the *uniformity of the meager ideal*, denoted $\operatorname{non}(\mathcal M)$ (or $\operatorname{non}(\mathcal B)$) is the least size of a non meager set of reals and the *almost disjointness number*, denoted $\mathfrak{a}$ is the least size of an infinite, almost disjoint family. The reverse inequality, $\mathfrak{a} < \operatorname{non}(\mathcal M)$ holds in many well studied models, for example the random model. I seem to remember reading that $\operatorname{non}(\mathcal M) < \mathfrak{a}$ is also consistent though I can't seem to find the reference now. Therefore my question is:

Is it consistent that $\operatorname{non}(\mathcal M) < \mathfrak{a}$ if so, what model does this hold in?

As a remark, such a model is necessarily a model of $\mathfrak{b} < \mathfrak{a}$ which I do know to be consistent in several models (though none of the constructions are particularly easy compared to those for $\mathcal{a} < \operatorname{non}(\mathcal M)$). Therefore a related question is in which (if any) of the models for $\mathfrak{b} < \mathfrak{a}$ has $\operatorname{non}(\mathcal M)$ been computed?

I would be also extremely interested in a model of $\mathfrak{b} < \operatorname{non}(\mathcal M) < \mathfrak{a}$ though I wouldn't be surprised if this consistency was not known (please correct me if I'm mistaken!).

Thanks!