The inhomogeneous Khintchine–Groshev conjecture in the critical cases

Let $n,m$ be positive integers with $nm=2$, let $\psi:\mathbb{N}\to\mathbb{R}_{\geq 0}$, and let $\mathbf{y}\in\mathbb{R}^m$. Let $\mathcal A_{n,m}^{\mathbf{y}}(\psi)$ denote the set of points satisfying the corresponding inhomogeneous Diophantine approximation condition, equipped with Lebesgue measure $|\cdot|$. The inhomogeneous Khintchine–Groshev conjecture. If

$$\sum_{q=1}^\infty q^{n-1}\psi(q)^m=\infty,$$

then

$$|\mathcal A_{n,m}^{\mathbf{y}}(\psi)|=1.$$

This is the remaining divergence question for the general inhomogeneous Khintchine–Groshev theorem without a monotonicity assumption when $nm=2$, namely the cases $(n,m)=(1,2)$ and $(2,1)$.