A construction of an iterated Ore extension

Let $B$ be a Poisson algebra $\mathbb{C}[x_1,\dots ,x_k]$ with Poisson bracket such that $$\{x_j,x_i\}=c_{ji}{x}_i{x}_j+p_{ji}$$ for all $j>i$, where $c_{ji}\in \mathbb{C}$ and $p_{ji}\in \mathbb{C}[x_1,\dots ,x_i]$. Here we obtain an iterated skew polynomial algebra such that its semiclassical limit is equal to $B$ and the results are illustrated by examples.