{"raw_statement":[{"iden":"problem statement","content":"We have an infinite hexagonal grid shown below.\n![image](https://img.atcoder.jp/abc269/b61b1e0469588c61352a7fa7f7865351.png)\nA hexagonal cell is represented as $(i,j)$ with two integers $i$ and $j$.  \nCell $(i,j)$ is adjacent to the following six cells:\n\n*   $(i-1,j-1)$\n*   $(i-1,j)$\n*   $(i,j-1)$\n*   $(i,j+1)$\n*   $(i+1,j)$\n*   $(i+1,j+1)$\n\nLet 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.  \nFor example, the distance between cells $(0,0)$ and $(1,1)$ is $1$, and the distance between cells $(2,1)$ and $(-1,-1)$ is $3$.\nYou are given $N$ cells $(X_1,Y_1),\\ldots,(X_N,Y_N)$.  \nHow 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 $D$?  \nFind the count modulo $998244353$."},{"iden":"constraints","content":"*   $1 \\leq N \\leq 300$\n*   $-10^9\\leq X_i,Y_i \\leq 10^9$\n*   $1\\leq D \\leq 10^{10}$\n*   $(X_i,Y_i)$ are pairwise distinct.\n*   All values in the input are integers."},{"iden":"input","content":"The input is given from Standard Input in the following format:\n\n$N$ $D$\n$X_1$ $Y_1$\n$\\vdots$\n$X_N$ $Y_N$"},{"iden":"sample input 1","content":"3 1\n0 0\n0 1\n1 0"},{"iden":"sample output 1","content":"5\n\nThere are five possible sets of the chosen cells: ${(0,0)},{(0,1)},{(1,0)},{(0,0),(0,1)}$, and ${(0,0),(1,0)}$."},{"iden":"sample input 2","content":"9 1\n0 0\n0 1\n0 2\n1 0\n1 1\n1 2\n2 0\n2 1\n2 2"},{"iden":"sample output 2","content":"33"},{"iden":"sample input 3","content":"5 10000000000\n314159265 358979323\n846264338 -327950288\n-419716939 937510582\n-97494459 -230781640\n628620899 862803482"},{"iden":"sample output 3","content":"31"}],"translated_statement":null,"sample_group":[],"show_order":["default"],"formal_statement":null,"simple_statement":null,"has_page_source":true}