[ICPC2020 Nanjing R] Interested in Skiing

### 题目描述 Kotori 对滑雪很感兴趣。滑雪场是在二维平面上沿着 $y$ 轴无限延伸的直线，其中场中的所有点 $(x,y)$ 满足 $-m\le x\le m$。滑雪时，Kotori 不能离开场地，这意味着他的 $x$ 坐标的绝对值应该始终不超过 $m$。地面上也有 $n$ 个路段是障碍，Kotori 无法越过障碍。 Kotori 将从 $(0, -10^{10^{10^{10^{10}}}})$ 开始滑雪（你可以将此 $y$ 坐标视为负无穷大），并朝着 $y$ 轴的正方向移动。她的垂直（平行于 $y$ 轴）速度始终是 $v_y$，此值不变，但是她可以在 $[-v_x, v_x]$ 的间隔内控制她的水平（平行于 $x$ 轴的）速度。Kotori 改变速度的时间可以忽略不计。 你的任务是帮助 Kotori 计算 $v_x^*$ 的最小值，即一旦 $v_x>v_x^*$，她就可以安全地穿过滑雪场而不会遇到障碍物。 ### 输入格式 每个测试文件中只有一个测试用例。 输入的第一行包含三个正整数 $n, m$ 和 $v_y$（$1\le n\le 100$，$1\le m\le 10^4$，$1\le v_y\le 10$），分别表示障碍物的数量、滑雪场的半宽和垂直速度。 对于下面的 $n$ 行，第 $i$ 行包含四个整数 $x_1, y_1, x_2$ 和 $y_2$（$-m\le x_1, x_2\le m$，$-10^4\le y_1, y_2\le 10^4$，$x_1\ne x_2$ 或 $y_1\ne y_2$），这四个整数表示第 $i$ 个障碍物，该障碍物是连接点 $(x_1, y_1)$ 和 $(x_2, y_2)$ 的线段，两者都包括在内（也就是说，这两个点也是障碍物的一部分，不能触摸）。保证没有两个障碍物相互交叉。 ### 输出格式 输出一行，其中包含一个数字，表示 $v_x^*$ 的最小值。如果 Kotori 无法通过滑雪场，请输出 `-1`（不带引号）。 当且仅当其绝对或相对误差不超过 $10^{-6}$ 时，您的答案才会被认为是正确的。 ------------ 翻译来自 [fire_wolf](https://www.luogu.com.cn/user/690669)。

Kotori is interested in skiing. The skiing field is an infinite strip going along $y$-axis on the 2-dimensional plane where all points $(x, y)$ in the field satisfies $-m \le x \le m$. When skiing, Kotori cannot move out of the field, which means that the absolute value of his $x$-coordinate should always be no more than $m$. There are also $n$ segments on the ground which are the obstacles and Kotori cannot move across the obstacles either. Kotori will start skiing from $(0, -10^{10^{10^{10^{10}}}})$ (you can regard this $y$-coordinate as a negative infinity) and moves towards the positive direction of the $y$-axis. Her vertical (parallel to the $y$-axis) speed is always $v_y$ which cannot be changed, however she can control her horizontal (parallel to the $x$-axis) speed in the interval of $[-v_x, v_x]$. The time that Kotori changes her velocity can be neglected. Your task is to help Kotori calculate the minimum value of $v_x^*$ that once $v_x>v_x^*$ she can safely ski through the skiing field without running into the obstacles.

There is only one test case in each test file. The first line of the input contains three positive integers $n$, $m$ and $v_y$ ($1 \le n \le 100$, $1 \le m \le 10^4$, $1 \le v_y \le 10$), indicating the number of obstacles, the half width of the skiing field and the vertical speed. For the following $n$ lines, the $i$-th line contains four integers $x_1$, $y_1$, $x_2$ and $y_2$ ($-m \le x_1, x_2 \le m$, $-10^4 \le y_1, y_2 \le 10^4$, $x_1 \ne x_2$ or $y_1 \ne y_2$) indicating the $i$-th obstacle which is a segment connecting point $(x_1, y_1)$ and $(x_2, y_2)$, both inclusive (that is to say, these two points are also parts of the obstacle and cannot be touched). It's guaranteed that no two obstacles intersect with each other.

Output one line containing one number indicating the minimum value of $v_x^*$. If it is impossible for Kotori to pass through the skiing field, output ``-1`` (without quotes) instead. Your answer will be considered correct if and only if its absolute or relative error does not exceed $10^{-6}$.

3 2 1
-2 0 1 0
-1 4 2 4
0 1 0 3

1.000000000000000

2 1 2
-1 0 1 0
1 1 0 1

-1

2 3 7
-3 0 2 2
3 1 -2 17

1.866666666666666

1 100 1
-100 0 99 0

0.000000000000000