CF50D.Bombing

The commanding officers decided to drop a nuclear bomb on the enemy's forces. You are ordered to determine the power of the warhead that needs to be used.

The enemy has N strategically important objects. Their positions are known due to the intelligence service. The aim of the strike is to deactivate at least K important objects of the enemy. The bombing impact point is already determined and has coordinates of [_X_0; _Y_0].

The nuclear warhead is marked by the estimated impact radius R ≥ 0. All the buildings that are located closer than R to the bombing epicentre will be destroyed. All the buildings that are located further than R from the epicentre, can also be deactivated with some degree of probability. Let's assume that D is the distance between a building and the epicentre. This building's deactivation probability P(D, R) is calculated according to the following formula:

We should regard as e__a, where e ≈ 2.7182818284590452353602874713527

If the estimated impact radius of the warhead is equal to zero, then all the buildings located in the impact point will be completely demolished and all the rest of important objects will not be damaged.

The commanding officers want the probability of failing the task to be no more than ε. Nuclear warheads are too expensive a luxury, that's why you have to minimise the estimated impact radius of the warhead.

指挥官决定对敌军部队投掷一枚核弹。你受命确定所需弹头的当量。

敌方拥有 $N$ 个具有战略重要性的目标，其位置已通过情报部门获取。此次打击的目标是使至少 $K$ 个敌方重要目标失效。轰炸的落点已确定，其坐标为 $[X_0; Y_0]$。

核弹头以预估杀伤半径 $R \geq 0$ 标定。所有与爆炸中心距离小于 $R$ 的建筑物将被彻底摧毁；而距离爆炸中心大于 $R$ 的建筑物，仍可能以一定概率失效。设某建筑物与爆炸中心的距离为 $D$，则该建筑物的失效概率 $P(D,\,R)$ 按如下公式计算：

其中， 应理解为 $e^a$，其中 $e \approx 2.7182818284590452353602874713527$。

若弹头预估杀伤半径为零，则恰好位于爆炸点处的所有建筑物将被完全摧毁，其余所有重要目标均不受损。

指挥官要求任务失败的概率不超过 $\varepsilon$。由于核弹头造价极其昂贵，因此你必须最小化弹头的预估杀伤半径 $R$。

The first line contains an integer N which represents the number of the enemy's objects (1 ≤ N ≤ 100). The second line contains two integers: K is the required number of deactivated objects, and ε is the maximally permitted probability of not completing the task, given in per mils (1 ≤ K ≤ N, 1 ≤ ε ≤ 999). The third line contains _X_0 and _Y_0 which are the coordinates of the strike impact point. The next N lines contain two numbers X__i and Y__i each which are the coordinates of every strategically important object. All the coordinates are integer, their absolute values do not exceed 1000.

Let us remind you that there are a thousand per mils in unity (number one).

There can be several objects in one point.

第一行包含一个整数 $N$，表示敌方目标的数量（$1 \leq N \leq 100$）。
第二行包含两个整数：$K$ 表示需要摧毁的目标数量，$\varepsilon$ 表示任务未能完成的允许最大概率（以千分之一为单位，即 per mils）（$1 \leq K \leq N$，$1 \leq \varepsilon \leq 999$）。
第三行包含两个整数 $X_0$ 和 $Y_0$，表示打击落点的坐标。
接下来的 $N$ 行，每行包含两个数 $X_i$ 和 $Y_i$，分别表示每个战略性重要目标的坐标。所有坐标的绝对值均不超过 $1000$，且均为整数。

请注意：$1$（即“一”）等于 $1000$ 个千分之一（per mils）。

同一坐标点上可能存在多个目标。

Print the sought estimated impact radius of the warhead. The absolute or relative measure of the inaccuracy of your answer should not exceed 10 - 6.

输出所求的弹头预估冲击半径。你的答案的绝对或相对误差不得超过 $10^{-6}$。