AT_icpc2013summer_warmingUp_g Moving Points

[problemUrl]: https://atcoder.jp/contests/jag2013summer-warmingup/tasks/icpc2013summer_warmingUp_g You are given $ N $ points in the $ xy $-plane. Each point is in a state of linear uniform motion. Your task is to calculate the distance to the furthest point in Manhattan distance from the origin at time $ t $. The first line of the input file contains the integers $ N $ and $ M $ ($ 1\ \leq\ N,\ M\ \leq\ 10^5 $), separated by a space. The next $ N $ lines describe the points. Each contains four real numbers $ x $, $ y $, $ vx $ and $ vy $ ($ |x|,|y|,|vx|,|vy|\ \leq\ 10^6 $). This shows the initial coordinates $ (x,\ y) $ and velocity $ (vx,\ vy) $. The next $ M $ lines describe the queries. Each line contains one real number $ t $ ($ 0\ \leq\ t\ \leq\ 10^6 $). For each query, output the maximal Manhattan distance in one line. The value which is accurate to within a relative or absolute value of 1E-9 will be accepted. ``` 2 2 0 0 1 0 1 0 -1 0 0 1 ``` ``` 1.0000000000 1.0000000000 ``` ``` 3 3 0 0 1 1 0 1 1 0 3 3 -2 -1 0 1 2 ``` ``` 6.0000000000 3.0000000000 4.0000000000 ``` ``` 3 3 1 1 0.5 0 0 2 1.5 -1 1.5 0 0 1 0 1 2 ``` ``` 2.0000000000 2.5000000000 3.5000000000 ```

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