Package for this problem was not updated by the problem writer or Codeforces administration after we’ve upgraded the judging servers. To adjust the time limit constraint, solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then value 800 ms will be displayed and used to determine the verdict.

Virtual contest is a way to take part in past contest, as close as possible to participation on time. It is supported only ICPC mode for virtual contests.
If you've seen these problems, a virtual contest is not for you - solve these problems in the archive.
If you just want to solve some problem from a contest, a virtual contest is not for you - solve this problem in the archive.
Never use someone else's code, read the tutorials or communicate with other person during a virtual contest.

No tag edit access

D. Bombing

time limit per test

2 secondsmemory limit per test

256 megabytesinput

standard inputoutput

standard outputThe 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:

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.

Input

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.

Output

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}.

Examples

Input

1

1 500

5 5

1 2

Output

3.84257761518762740

Input

5

3 100

0 0

3 4

60 70

100 100

10 10

5 12

Output

13.45126176453737600

Codeforces (c) Copyright 2010-2019 Mike Mirzayanov

The only programming contests Web 2.0 platform

Server time: Nov/22/2019 22:26:48 (h1).

Desktop version, switch to mobile version.

Supported by

User lists

Name |
---|