Remnants of continuants with large fixed endings

To each finite word in the finite alphabet $\mathbf{A}\subseteq\mathbb{N}$, we add the prefix $V$ and the ending $W$ — some fixed finite words in the alphabet $\mathbb{N}$. The resulting words are associated with decompositions into finite continued fractions of some rational numbers from the range $(0,1)$. For these rationalities , consider irreducible denominators; the set of those that do not exceed a certain increasing value $N\in\mathbb{N}$, denoted by $\mathfrak{D}^{N}_{\mathbf{A},V,W}$. In the author's previous work, it was proved that under certain conditions on $Q$ for not very large $V$ and $W$ plenty $\mathfrak{D}^{N}_{\mathbf{A},V,W}$ contains almost all possible deductions modulo $Q$ and this formula has a power reduction. In this paper, a similar formula is obtained for an arbitrarily large $W$.