Distinction criterion for generic induced representations of $GL(n,K)$

Let $G_m(K)=GL(m,K)$. Let $(n_1,\dots,n_t)$ be a partition of $n$, and for each $i$ let $\Delta_i$ be a quasi-square-integrable representation of $G_{n_i}(K)$. Let $\pi$ be the generic representation of $G_n(K)$ obtained by normalized parabolic induction of the $\Delta_i$.

Distinction conjecture. The representation $\pi$ is distinguished if and only if, after reordering the $\Delta_i$, there is an integer $r$ between $1$ and $t/2$ such that

$$\Delta_{i+1}^{\sigma}=\Delta_i^{\vee}$$

for $i=1,3,\dots,2r-1$, and $\Delta_i$ is distinguished for $i>2r$.

This is presented as an expected generalization of known distinction results for discrete-series and principal-series representations. The source does not provide a proof or a resolution.