Now that all the presents have been delivered, the North Pole is finally at peace — and it's time to celebrate with a spectacular New Year's fireworks show! The North Pole is modeled as the Cartesian plane, with (n) cities located at distinct lattice points. You are also given an integer (k). For a proper subset(^{\text{∗}}) (T) of the cities ((T) may be empty), we define its explosiveness as follows: A firework is launched from every city in (T). For each city (c) not in (T), let (f) be the number of fireworks launched from cities that are exactly (\sqrt{k}) Euclidean distance(^{\text{†}}) away from (c). Assign the number ((f+1)) to this city (c). The explosiveness of (T) is the product of all numbers assigned in Step 2. Compute the sum of the explosiveness of (T) over all (2^n-1) proper subsets (T) of the cities. Since the answer may be large, output it modulo (998\,244\,353). (^{\text{∗}})A proper subset is any subset which is not equal to the whole set. (^{\text{†}})The Euclidean distance between two points ((x, y)) and ((p, q)) is defined as (\sqrt{(x - p)^2 + (y - q)^2}). Each test contains multiple test cases. The first line contains the number of test cases (t) ((1 \le t \le 1000)). The description of the test cases follows. The first line of each test case contains two integers (n) and (k) ((2\le n\le 31), (1\leq k \leq2\cdot 10^4)). Then (n) lines follow, the (i)-th line containing two integers (x_i) and (y_i) ((1\leq x_i, y_i\leq 100)) — the (x) and (y) coordinates of the (i)-th city, respectively. It is guaranteed that the coordinates of the cities are pairwise distinct. It is guaranteed that the sum of (n^3) over all test cases does not exceed (31^3). For each test case, print a single integer — the sum, modulo (998\,244\,353), of the explosiveness over all proper subsets (T) of