Is there a model of set theory in which $\mathfrak p< \mathfrak b < \mathfrak q$?

Here $\mathfrak p$, $\mathfrak b$, $\mathfrak q$ are small uncountable cardinals:

- $\mathfrak p$ is the smallest cardinality of any family $\mathcal F \subseteq [\omega]^\omega$, which has the strong finite intersection property, but does not have a pseudo intersection;
- $\mathfrak b$ is the bounding number;
$\mathfrak q = \min\{\kappa :\text{ no subset }X \subseteq \mathbb R\text{ of cardinality }|X| \ge κ\text{ is a Q-set}\}$.

- $\min\{\mathfrak b, \mathfrak q \}\in \{\mathfrak p,\mathfrak q \}$ ?