CF645G.Armistice Area Apportionment

After a drawn-out mooclear arms race, Farmer John and the Mischievous Mess Makers have finally agreed to establish peace. They plan to divide the territory of Bovinia with a line passing through at least two of the n outposts scattered throughout the land. These outposts, remnants of the conflict, are located at the points (_x_1, _y_1), (_x_2, _y_2), ..., (x__n, y__n).

In order to find the optimal dividing line, Farmer John and Elsie have plotted a map of Bovinia on the coordinate plane. Farmer John's farm and the Mischievous Mess Makers' base are located at the points P = (a, 0) and Q = ( - a, 0), respectively. Because they seek a lasting peace, Farmer John and Elsie would like to minimize the maximum difference between the distances from any point on the line to P and Q.

Formally, define the difference of a line relative to two points P and Q as the smallest real number d so that for all points X on line , |PX - QX| ≤ d. (It is guaranteed that d exists and is unique.) They wish to find the line passing through two distinct outposts (x__i, y__i) and (x__j, y__j) such that the difference of relative to P and Q is minimized.

在一场旷日持久的“核武”竞赛之后，农夫约翰与捣蛋鬼制造者们终于同意缔结和平。他们计划用一条至少经过 n 个哨所中两个哨所的直线来划分波维尼亚（Bovinia）的领土。这些哨所是冲突遗留下来的遗迹，其坐标分别为 (_x_₁, _y_₁), (_x_₂, _y_₂), ..., (x__n, y__n)。

为了找到最优的分界线，农夫约翰与埃尔西已在坐标平面上绘制了波维尼亚的地图。农夫约翰的农场与捣蛋鬼制造者们的基地分别位于点 P = (a, 0) 和 Q = ( - a, 0)。由于他们渴望长久的和平，农夫约翰与埃尔西希望最小化该直线上任意一点到 P 与 Q 的距离之差的最大值。

形式化地，定义一条直线 关于两点 P 和 Q 的差值为最小的实数 d，使得对直线 上任意一点 X，均有 |PX - QX| ≤ d。（可以保证这样的 d 存在且唯一。）他们希望找到一条经过两个不同哨所 (x__i, y__i) 和 (x__j, y__j) 的直线 ，使得该直线 关于 P 和 Q 的差值最小。

The first line of the input contains two integers n and a (2 ≤ n ≤ 100 000, 1 ≤ a ≤ 10 000) — the number of outposts and the coordinates of the farm and the base, respectively.

The following n lines describe the locations of the outposts as pairs of integers (x__i, y__i) (|x__i|, |y__i| ≤ 10 000). These points are distinct from each other as well as from P and Q.

输入的第一行包含两个整数 $n$ 和 $a$（$2 \leq n \leq 100\,000$，$1 \leq a \leq 10\,000$），分别表示前哨站的数量、农场与基地的坐标。

接下来的 $n$ 行每行描述一个前哨站的位置，以一对整数 $(x_i,\,y_i)$ 给出（$|x_i|,\,|y_i| \leq 10\,000$）。这些点互不相同，且均不同于点 $P$ 和 $Q$。

Print a single real number—the difference of the optimal dividing line. Your answer will be considered correct if its absolute or relative error does not exceed 10 - 6.

Namely: let's assume that your answer is a, and the answer of the jury is b. The checker program will consider your answer correct, if .

输出一个实数——最优分割线的差值。若你的答案的绝对误差或相对误差不超过 $10^{-6}$，则视为正确。

即：假设你的答案为 $a$，评测组的答案为 $b$。当满足 时，评测程序将判定你的答案正确。

In the first sample case, the only possible line is y = x - 1. It can be shown that the point X which maximizes |PX - QX| is (13, 12), with , which is .

In the second sample case, if we pick the points (0, 1) and (0,  - 3), we get as x = 0. Because PX = QX on this line, the minimum possible difference is 0.

在第一个样例中，唯一可能的直线 是 $y = x - 1$。可以证明，使 $|PX - QX|$ 最大的点 $X$ 为 $(13,\,12)$，此时 ，即 。

在第二个样例中，若选取点 $(0,\,1)$ 和 $(0,\,-3)$，则得到直线 为 $x = 0$。由于在此直线上恒有 $PX = QX$，因此可能的最小差值为 $0$。