Coffee-Central

Alg. ans Problem E Coffee Central Problem ID: coffee Isitjustafadorisitheretostay? Apparently, people have become so addicted to coffee that apartments that are close to many coffee shops will actually fetch higher rents. This has come to the attention of a local real-estate company. They are interested in identifying the most valuable locations in the city in terms of their proximity to large numbers of coffee shops. They have given you a map of the city, marked with the locations of coffee shops. Assuming that the average person is willing to walk only a fixed number of blocks for their morning coffee, you have to find the location from which one can reach the largest number of coffee shops. As you are probably aware, your hometown is built on a square grid layout, with blocks aligned on north-south and east-west axes. Since you have to walk along streets, the distance between intersections (a,b) and (c,d) is|a−c|+|b−d|. Input The input contains several test cases. Each test case describes a city. The first line of each test case contains four integers dx, dy, n, and q. These are the dimensions of the city grid dx×dy (1 ≤ dx,dy ≤ 1000), the number of coffee shops n (0 ≤ n ≤ 5·105), and the number of queries q (1 ≤ q ≤ 20). Each of the next n lines contains two integers xi and yi (1 ≤ xi ≤ dx, 1 ≤ yi ≤ dy); thesespecifythelocationofthe ith coffeeshop. Therewillbeatmost one coffee shop per intersection. Each of the next q lines contains a single integer m (0 ≤ m ≤ 106), the maximal distance that a person is willing to walk for a cup of coffee. The last test case is followed by a line containing four zeros. Output For each test case in the input, display its case number. Then display one line per query in the test case. Each line displays the maximum number of coffee shops reachable for the given query distance m followed by the optimal location. Forexample,thesampleoutputshowsthat3coffeeshopsarewithinquerydistance1oftheoptimallocation (3,4), 4shopsarewithinquerydistance2ofoptimallocation(2,2),and5shopsarewithinquerydistance4ofoptimal location (3,1). Iftherearemultipleoptimallocations,pickthelocationthatisfurthestsouth(minimalpositiveinteger y-coordinate). If there is still a tie, pick the location furthest west (minimal positive integer x-coordinate).