CF1575B.Building an Amusement Park

Mr. Chanek lives in a city represented as a plane. He wants to build an amusement park in the shape of a circle of radius $r$. The circle must touch the origin (point $(0, 0)$).

There are $n$ bird habitats that can be a photo spot for the tourists in the park. The $i$-th bird habitat is at point $p_i = (x_i, y_i)$.

Find the minimum radius $r$ of a park with at least $k$ bird habitats inside.

A point is considered to be inside the park if and only if the distance between $p_i$ and the center of the park is less than or equal to the radius of the park. Note that the center and the radius of the park do not need to be integers.

In this problem, it is guaranteed that the given input always has a solution with $r \leq 2 \cdot 10^5$.

陈先生生活在一个以平面表示的城市中。他希望建造一个半径为 $r$ 的圆形游乐园。该圆必须与原点（即点 $(0, 0)$）相切。

共有 $n$ 个鸟类栖息地，可作为游乐园内游客的拍照景点。第 $i$ 个鸟类栖息地位于点 $p_i = (x_i, y_i)$。

请找出满足至少包含 $k$ 个鸟类栖息地的游乐园的最小半径 $r$。

当且仅当点 $p_i$ 到游乐园中心的距离小于或等于游乐园半径时，该点才被视为在游乐园内部。注意：游乐园的中心坐标和半径不一定是整数。

本题保证输入数据总存在一个解，且满足 $r \leq 2 \cdot 10^5$。

The first line contains two integers $n$ and $k$ ($1 \leq n \leq 10^5$, $1 \leq k \leq n$) — the number of bird habitats in the city and the number of bird habitats required to be inside the park.

The $i$-th of the next $n$ lines contains two integers $x_i$ and $y_i$ ($0 \leq |x_i|, |y_i| \leq 10^5$) — the position of the $i$-th bird habitat.

第一行包含两个整数 $n$ 和 $k$（$1 \leq n \leq 10^5$，$1 \leq k \leq n$）—— 分别表示城市中鸟类栖息地的数量以及公园内必须包含的鸟类栖息地数量。

接下来的 $n$ 行中，第 $i$ 行包含两个整数 $x_i$ 和 $y_i$（$0 \leq |x_i|, |y_i| \leq 10^5$）—— 表示第 $i$ 个鸟类栖息地的位置。

Output a single real number $r$ denoting the minimum radius of a park with at least $k$ bird habitats inside. It is guaranteed that the given input always has a solution with $r \leq 2 \cdot 10^5$.

Your answer is considered correct if its absolute or relative error does not exceed $10^{-4}$.

Formally, let your answer be $a$, and the jury's answer be $b$. Your answer is accepted if and only if $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-4}$.

输出一个实数 $r$，表示包含至少 $k$ 个鸟类栖息地的公园的最小半径。保证给定输入总存在满足 $r \leq 2 \cdot 10^5$ 的解。

若你的答案的绝对误差或相对误差不超过 $10^{-4}$，则视为正确。

形式化地，设你的答案为 $a$，评测机的答案为 $b$。当且仅当 $\frac{|a - b|}{\max{(1, |b|)}} \le 10^{-4}$ 时，你的答案被接受。

In the first example, Mr. Chanek can put the center of the park at $(-3, -1)$ with radius $\sqrt{10} \approx 3.162$. It can be proven this is the minimum $r$.

The following illustrates the first example. The blue points represent bird habitats and the red circle represents the amusement park.

在第一个例子中，Chanek 先生可以将公园的中心设在 $(-3, -1)$，半径为 $\sqrt{10} \approx 3.162$。可以证明这是最小的 $r$。

以下图示展示了第一个例子：蓝色点表示鸟类栖息地，红色圆圈表示游乐园。