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: 

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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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.math.BigInteger;
import java.util.Arrays;
import java.util.InputMismatchException;

/**
 * @author Egor Kulikov (egor@egork.net)
 */
public class TaskD {
	@SuppressWarnings({"FieldCanBeLocal", "UnusedDeclaration"})
	InputReader in;
	PrintWriter out;

	void solve() {
		int n = in.readInt();
		int k = in.readInt();
		int epsilon = in.readInt();
		int x0 = in.readInt();
		int y0 = in.readInt();
		int[] squaredDistance = new int[n];
		int maxDistSquared = 0;
		for (int i = 0; i < n; i++) {
			int x = in.readInt();
			int y = in.readInt();
			maxDistSquared = Math.max(squaredDistance[i] = (x0 - x) * (x0 - x) + (y0 - y) * (y0 - y), maxDistSquared);
		}
		double left = 0;
		double right = Math.sqrt(maxDistSquared);
		double[][] destroyedProbability = new double[n + 1][k + 1];
		while (right - left > 1e-8) {
			double curDist = (left + right) / 2;
			double curDistSquared = curDist * curDist;
			Arrays.fill(destroyedProbability[0], 0);
			destroyedProbability[0][0] = 1;
			for (int i = 0; i < n; i++) {
				double probabilityToDestroy = curDistSquared > squaredDistance[i] ? 1 : Math.exp(1 - squaredDistance[i] / curDistSquared);
				Arrays.fill(destroyedProbability[i + 1], 0);
				for (int j = 0; j < k; j++) {
					destroyedProbability[i + 1][j] += (1 - probabilityToDestroy) * destroyedProbability[i][j];
					destroyedProbability[i + 1][j + 1] += probabilityToDestroy * destroyedProbability[i][j];
				}
				destroyedProbability[i + 1][k] += destroyedProbability[i][k];
			}
			if (destroyedProbability[n][k] * 1000 > 1000 - epsilon)
				right = curDist;
			else
				left = curDist;
		}
		double ans = (left + right) / 2;
		out.printf("%.7f\n", ans);
	}

	public static void main(String[] args) {
		new TaskD().run();
	}

	TaskD() {
		@SuppressWarnings({"UnusedDeclaration"})
		String id = getClass().getName().toLowerCase();
		//noinspection EmptyTryBlock
		try {
//			System.setIn(new FileInputStream(id + ".in"));
//			System.setOut(new PrintStream(new FileOutputStream(id + ".out")));
//			System.setIn(new FileInputStream("input.txt"));
//			System.setOut(new PrintStream(new FileOutputStream("output.txt")));
		} catch (Exception e) {
			throw new RuntimeException(e);
		}
		in = new InputReader(System.in);
		out = new PrintWriter(System.out);
	}

	void run() {
		//noinspection InfiniteLoopStatement
		solve();
		exit();
	}

	@SuppressWarnings({"UnusedDeclaration"})
	void exit() {
		out.close();
		System.exit(0);
	}

	@SuppressWarnings({"UnusedDeclaration"})
	static class InputReader {
		InputStream stream;
		byte[] buf = new byte[1024];
		int curChar, numChars;

		InputReader(InputStream stream) {
			this.stream = stream;
		}

		int read() {
			if (numChars == -1)
				throw new InputMismatchException();
			if (curChar >= numChars) {
				curChar = 0;
				try {
					numChars = stream.read(buf);
				} catch (IOException e) {
					throw new InputMismatchException();
				}
				if (numChars <= 0)
					return -1;
			}
			return buf[curChar++];
		}

		int readInt() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			int res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		long readLong() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			long res = 0;
			do {
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			} while (!isSpaceChar(c));
			return res * sgn;
		}

		String readString() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			StringBuffer res = new StringBuffer();
			do {
				res.appendCodePoint(c);
				c = read();
			} while (!isSpaceChar(c));
			return res.toString();
		}

		boolean isSpaceChar(int c) {
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		String readLine0() {
			StringBuffer buf = new StringBuffer();
			int c = read();
			while (c != '\n' && c != -1) {
				if (c != '\r')
					buf.appendCodePoint(c);
				c = read();
			}
			return buf.toString();
		}

		String readLine() {
			String s = readLine0();
			while (s.trim().length() == 0)
				s = readLine0();
			return s;
		}

		String readLine(boolean ignoreEmptyLines) {
			if (ignoreEmptyLines)
				return readLine();
			else
				return readLine0();
		}

		BigInteger readBigInteger() {
			try {
				return new BigInteger(readString());
			} catch (NumberFormatException e) {
				throw new InputMismatchException();
			}
		}

		char readCharacter() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			return (char) c;
		}

		double readDouble() {
			int c = read();
			while (isSpaceChar(c))
				c = read();
			int sgn = 1;
			if (c == '-') {
				sgn = -1;
				c = read();
			}
			double res = 0;
			while (!isSpaceChar(c) && c != '.') {
				if (c == 'e' || c == 'E')
					return res * Math.pow(10, readInt());
				if (c < '0' || c > '9')
					throw new InputMismatchException();
				res *= 10;
				res += c - '0';
				c = read();
			}
			if (c == '.') {
				c = read();
				double m = 1;
				while (!isSpaceChar(c)) {
					if (c == 'e' || c == 'E')
						return res * Math.pow(10, readInt());
					if (c < '0' || c > '9')
						throw new InputMismatchException();
					m /= 10;
					res += (c - '0') * m;
					c = read();
				}
			}
			return res * sgn;
		}
	}
}