Problem: The heat during the last few days has been really intense. Scientists from all over the Berland study how the temperatures and weather change, and they claim that this summer is abnormally hot. But any scientific claim sounds a lot more reasonable if there are some numbers involved, so they have decided to actually calculate some value which would represent how high the temperatures are.

Mathematicians of Berland State University came up with a special heat intensity value. This value is calculated as follows:

Suppose we want to analyze the segment of n consecutive days. We have measured the temperatures during these n days; the temperature during i-th day equals a_i.

We denote the average temperature of a segment of some consecutive days as the arithmetic mean of the temperature measures during this segment of days. So, if we want to analyze the average temperature from day x to day y, we calculate it as \frac{∑ _{i = x}^{y} a_i}{y - x + 1} (note that division is performed without any rounding). The heat intensity value is the maximum of average temperatures over all segments of not less than k consecutive days. For example, if analyzing the measures [3, 4, 1, 2] and k = 3, we are interested in segments [3, 4, 1], [4, 1, 2] and [3, 4, 1, 2] (we want to find the maximum value of average temperature over these segments).

You have been hired by Berland State University to write a program that would compute the heat intensity value of a given period of days. Are you up to this task?

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 5000) — the number of days in the given period, and the minimum number of days in a segment we consider when calculating heat intensity value, respectively.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ 5000) — the temperature measures during given n days.

Output

Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than k consecutive days.

Your answer will be considered correct if the following condition holds: |res - res_0| < 10^{-6}, where res is your answer, and res_0 is the answer given by the jury's solution.

Example

Input

4 3
3 4 1 2


Output

2.666666666666667

Solution (in JAVA):

Solution:
import java.util.*;

import java.io.*;

public class temppp {

	public static void main(String[] args) {

		// TODO Auto-generated method stub

		FastInputReader s = new FastInputReader();
		int n = s.nextInt();
		int k = s.nextInt();
		int[] arr = new int[n];
		for(int i=0;i<n;i++) {
			arr[i] = s.nextInt();
		}
		double max = 0;
		double sum = 0;
		for(int i=0;i<n-k+1;i++) {
			int count = 0;
			sum=0;
			for(int j=i;j<n;j++) {
				count++;
				sum+=arr[j];
				if(count>=k) {
					max=Math.max(max,sum/count);
				}
			}
		}
		
		
		System.out.println(max);
	}

	public static class FastInputReader {

		private byte[] buf = new byte[16384];

		private int curChar;

		private int numChars;

		public int read() {

			if (numChars == -1)

				throw new InputMismatchException();

			if (curChar >= numChars) {

				curChar = 0;

				try {

					numChars = System.in.read(buf);

				} catch (IOException e) {

					throw new InputMismatchException();

				}

				if (numChars <= 0)

					return -1;

			}

			return buf[curChar++];

		}

		public String nextLine() {

			int c = read();

			while (isSpaceChar(c))

				c = read();

			StringBuilder res = new StringBuilder();

			do {

				res.appendCodePoint(c);

				c = read();

			} while (!isEndOfLine(c));

			return res.toString();

		}

		public String nextString() {

			int c = read();

			while (isSpaceChar(c))

				c = read();

			StringBuilder res = new StringBuilder();

			do {

				res.appendCodePoint(c);

				c = read();

			} while (!isSpaceChar(c));

			return res.toString();

		}

		public long nextLong() {

			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;

		}

		public int nextInt() {

			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;

		}

		public int[] nextIntArray(int n) {

			int[] arr = new int[n];

			for (int i = 0; i < n; i++) {

				arr[i] = nextInt();

			}

			return arr;

		}

		public long[] nextLongArray(int n) {

			long[] arr = new long[n];

			for (int i = 0; i < n; i++) {

				arr[i] = nextLong();

			}

			return arr;

		}

		private boolean isSpaceChar(int c) {

			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;

		}

		private boolean isEndOfLine(int c) {

			return c == '\n' || c == '\r' || c == -1;

		}

	}

	public static class MyScanner {

		BufferedReader reader;

		public MyScanner() {

			this.reader = new BufferedReader(new InputStreamReader(System.in));

		}

		public void close() throws IOException {

			this.reader.close();

		}

		int nextInt() {

			return Integer.parseInt(this.next());

		}

		long nextLong() {

			return Long.parseLong(this.next());

		}

		float nextFloat() {

			return Float.parseFloat(this.next());

		}

		double nextDouble() {

			return Double.parseDouble(this.next());

		}

		String next() {

			String str = "";

			try {

				str = this.reader.readLine().trim();

			} catch (IOException e) {

				e.printStackTrace();

			}

			return str;

		}

		String[] nextStringArray() {

			String[] str = null;

			try {

				str = this.reader.readLine().trim().split(" ");

			} catch (IOException e) {

				e.printStackTrace();

			}

			return str;

		}

		int[] nextIntArray() {

			String[] data = nextStringArray();

			int[] a = new int[data.length];

			for (int i = 0; i < a.length; i++) {

				a[i] = Integer.parseInt(data[i]);

			}

			return a;

		}

		Integer[] nextIntegerArray() {

			String[] data = nextStringArray();

			Integer[] a = new Integer[data.length];

			for (int i = 0; i < a.length; i++) {

				a[i] = Integer.parseInt(data[i]);

			}

			return a;

		}

		long[] nextLongArray() {

			String[] data = nextStringArray();

			long[] a = new long[data.length];

			for (int i = 0; i < a.length; i++) {

				a[i] = Long.parseLong(data[i]);

			}

			return a;

		}

		float[] nextFloatArray() {

			String[] data = nextStringArray();

			float[] a = new float[data.length];

			for (int i = 0; i < a.length; i++) {

				a[i] = Float.parseFloat(data[i]);

			}

			return a;

		}

		double[] nextDoubleArray() {

			String[] data = nextStringArray();

			double[] a = new double[data.length];

			for (int i = 0; i < a.length; i++) {

				a[i] = Double.parseDouble(data[i]);

			}

			return a;

		}

	}

}