Problem: 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 [X0; Y0].

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: 

<image> We should regard <image> as ea, 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. 

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 X0 and Y0 which are the coordinates of the strike impact point. The next N lines contain two numbers Xi and Yi 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

Solution (in JAVA):

Solution:

import java.io.BufferedReader;
import java.io.FileNotFoundException;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.Arrays;
import java.util.HashSet;
import java.util.StringTokenizer;

/**
 *
 *
 * 3 2 3 5
 * -2 -1 4 -1 2 7 3
 *
 *
 * @author pttrung
 */
public class D {

    public static long MOD = 100000000;
    public static double [][]dp;

    public static void main(String[] args) throws FileNotFoundException {
        PrintWriter out;

        Scanner in = new Scanner();
        //out = new PrintWriter(new FileOutputStream(new File("output.txt")));
        out = new PrintWriter(System.out);

        int n = in.nextInt();
        int k = in.nextInt();
        int e = in.nextInt();
        Point root = new Point(in.nextInt(), in.nextInt());
        double[] data = new double[n];
        for (int i = 0; i < n; i++) {
            Point p = new Point(in.nextInt(), in.nextInt());
            data[i] = dist(root, p);
        }
        Arrays.sort(data);
        double start = 0;
        double end = data[n - 1];
        int left = n - k;
        dp = new double[n][left + 1];
        while (Math.abs(start - end) > 1e-9) {
            double mid = (start + end) / 2;
            double[] p = new double[n];
            for (int i = 0; i < n; i++) {
                if (mid >= data[i]) {
                    p[i] = 1;
                } else {
                    p[i] =  Math.exp(1 - (data[i] * data[i] / (mid * mid)));
                }
               //  out.println(p[i] + " " + mid);
            }
            for(double []a : dp){
                Arrays.fill(a,-1);
            }
            double prob = cal(0, left, p);

            if (prob * 1000 < 1000 - e) {
                start = mid;
            } else {
                end = mid;
            }
           // out.println("Prob " + prob * 1000 + " " + start + " " + end);
        }
        out.println(start);
        out.close();

    }

    public static double cal(int index, int left, double[] p) {
        if (index == p.length) {
            return 1;
        }
        if(dp[index][left] != -1){
            return dp[index][left];
        }
        
        double result = (double) p[index] * cal(index + 1, left, p);
        if (left > 0) {
            result += (1 - p[index]) * cal(index + 1, left - 1, p);
        }
        return dp[index][left] = result;

    }

    public static double dist(Point a, Point b) {
        double val = (a.x - b.x) * (a.x - b.x) + (a.y - b.y) * (a.y - b.y);
        return Math.sqrt(val);
    }

    public static double dist(long a, long b, long x, long y) {
        double val = (b - a) * (b - a) + (x - y) * (x - y);
        val = Math.sqrt(val);
        double other = x * x + a * a;
        other = Math.sqrt(other);
        return val + other;
    }

    public static class Point {

        int x, y;

        public Point(int x, int y) {
            this.x = x;
            this.y = y;
        }
    }

    public static class FT {

        int[] data;

        FT(int n) {
            data = new int[n];
        }

        public void update(int index, int value) {
            while (index < data.length) {
                data[index] += value;
                index += (index & (-index));
            }
        }

        public int get(int index) {
            int result = 0;
            while (index > 0) {
                result += data[index];
                index -= (index & (-index));
            }
            return result;

        }
    }

    public static class Sign {

        char c;
        int x, y;

        public Sign(char c, int x, int y) {
            this.c = c;
            this.x = x;
            this.y = y;
        }
    }

    public static long gcd(long a, long b) {
        if (b == 0) {
            return a;
        }
        return gcd(b, a % b);
    }

    public static long pow(long a, long b) {
        if (b == 0) {
            return 1;
        }
        if (b == 1) {
            return a;
        }
        long val = pow(a, b / 2);
        if (b % 2 == 0) {
            return val * val % MOD;
        } else {
            return val * (val * a % MOD) % MOD;
        }
    }

    static class Scanner {

        BufferedReader br;
        StringTokenizer st;

        public Scanner() throws FileNotFoundException {
            // System.setOut(new PrintStream(new BufferedOutputStream(System.out), true));
            br = new BufferedReader(new InputStreamReader(System.in));
            //br = new BufferedReader(new InputStreamReader(new FileInputStream(new File("input.txt"))));
        }

        public String next() {

            while (st == null || !st.hasMoreTokens()) {
                try {
                    st = new StringTokenizer(br.readLine());
                } catch (Exception e) {
                    throw new RuntimeException();
                }
            }
            return st.nextToken();
        }

        public long nextLong() {
            return Long.parseLong(next());
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public double nextDouble() {
            return Double.parseDouble(next());
        }

        public String nextLine() {
            st = null;
            try {
                return br.readLine();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }

        public boolean endLine() {
            try {
                String next = br.readLine();
                while (next != null && next.trim().isEmpty()) {
                    next = br.readLine();
                }
                if (next == null) {
                    return true;
                }
                st = new StringTokenizer(next);
                return st.hasMoreTokens();
            } catch (Exception e) {
                throw new RuntimeException();
            }
        }
    }
}