Do Use Hexagon Grid 2

We have an infinite hexagonal grid shown below.  A hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$. Cell $(i,j)$ is adjacent to the following six cells: * $(i-1,j-1)$ * $(i-1,j)$ * $(i,j-1)$ * $(i,j+1)$ * $(i+1,j)$ * $(i+1,j+1)$ Let us define the distance between two cells $X$ and $Y$ by the minimum number of moves required to travel from cell $X$ to cell $Y$ by repeatedly moving to an adjacent cell. For example, the distance between cells $(0,0)$ and $(1,1)$ is $1$, and the distance between cells $(2,1)$ and $(-1,-1)$ is $3$. You are given $N$ cells $(X_1,Y_1),\ldots,(X_N,Y_N)$. How many ways are there to choose one or more from these $N$ cells so that the distance between any two of the chosen cells is at most $D$? Find the count modulo $998244353$. ## Constraints * $1 \leq N \leq 300$ * $-10^9\leq X_i,Y_i \leq 10^9$ * $1\leq D \leq 10^{10}$ * $(X_i,Y_i)$ are pairwise distinct. * All values in the input are integers. ## Input The input is given from Standard Input in the following format: $N$ $D$ $X_1$ $Y_1$ $\vdots$ $X_N$ $Y_N$ [samples]