问题标题: 酷町堂：很简单的题，🍳煎蛋，对了我给70豆

6111   CF799G Cut the pie

题目描述 Description

Arkady reached the nn -th level in Township game, so Masha decided to bake a pie for him! Of course, the pie has a shape of convex nn -gon, i.e. a polygon with nn vertices.
Arkady decided to cut the pie in two equal in area parts by cutting it by a straight line, so that he can eat one of them and give the other to Masha. There is a difficulty because Arkady has already put a knife at some point of the pie, so he now has to cut the pie by a straight line passing trough this point.
Help Arkady: find a line that passes through the point Arkady has put a knife into and cuts the pie into two parts of equal area, or determine that it’s impossible. Your program has to quickly answer many queries with the same pie, but different points in which Arkady puts a knife.

输入描述 Input Description

The first line contains two integers nn and qq ( 3<=n<=10^{4}3<=n<=104 , 1<=q<=10^{5}1<=q<=105 ) — the number of vertices in the pie and the number of queries.
nn line follow describing the polygon vertices in clockwise order. The ii -th of these line contains two integers x_{i}xi​ and y_{i}yi​ ( -10^{6}<=x_{i},y_{i}<=10^{6}−106<=xi​,yi​<=106 ) — the coordinates of the ii -th vertex. It is guaranteed that the polygon is strictly convex, in particular, no three vertices line on the same line.
An empty line follows.
qq lines follow describing the query points. The ii -th of these lines contain two integers x_{i}xi​ and y_{i}yi​ ( -10^{6}<=x_{i},y_{i}<=10^{6}−106<=xi​,yi​<=106 ) — the coordinates of the point in which Arkady puts the knife in the ii -th query. In is guaranteed that in each query the given point is strictly inside the polygon, in particular, is not on its edges.

输出描述 Output Description

For each query print single integer — the polar angle of the line that is the answer for the corresponding query, in radians. The angle should be in the segment [0;π][0;π] , the angles are measured from the direction of OXOX axis in counter-clockwise order. For example, the polar angle of the OYOY axis is . If there is no answer in that query, print -1.
If there are several answers, print any of them. Your answer is considered correct if the difference between the areas of the parts divided by the total area of the polygon doesn’t exceed 10^{-4}10−4 by absolute value. In other words, if aa and bb are the areas of the parts after the cut, then your answer is correct if and only of .

样例输入 Sample Input

输入 #1 3 1 0 0 0 3 3 0 1 1 ########### 输入 #2 5 3 6 5 6 3 5 0 0 0 0 5 5 4 3 3 5 2

样例输出 Sample Output

输出 #1 2.67794504460098710000 ########### 输出 #2 0.60228734612690049000 1.27933953226473580000 2.85805511179015910000

RemoteJudge

您提交的代码将被发送回原 OJ 进行测评，并由酷町堂抓取其测评结果。
将使用公用账户进行测评，建议您 绑定个人账户，使用自己在原 OJ 的账户提交测评。

题目描述

有一个nn边形，其中nn个顶点的坐标都已经给出。有qq次询问，每次询问都给出一个点的坐标，你需要过这个定点把这个nn边形切成面积相等的两部分，我们称这条线为等分线。对于每次询问，输出一个数，为等分线由xx坐标轴逆时针转动的角度，用弧度制输出。比如说，等分线为yy轴，那么你应该输出1.57079632679489661923132169163981.5707963267948966192313216916398，因为yy轴是由xx轴逆时针转动9090°而得，化为弧度制即为π/2π/2。

输入格式：

第一行两个整数nn和qq；
接下来nn行，一行输入22个数，为这个nn边形nn个点的坐标；
再接下来qq行，一行输入22个数，为每次询问的定点的坐标。

输出格式：

一共qq行，每行为每次询问的结果。如果过这个点无法将这个nn边形切成面积相同的两块，输出-1−1。

数据测试点范围：

33<=nn<=10^4104，11<=qq<=10^5105，所有点的坐标（包括nn边形的顶点坐标以及每次询问的定点坐标）都满足：-10^6−106<=x,yx,y<=10^6106

说明/提示

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