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.lang.*;
import java.io.*;

public class Codechef
{
   
    //static boolean vis[];
    int max = (int)1e5+1;
    static ArrayList<Integer>graph[];
    static int q_v[];
    static ArrayList<Integer>qs[];
    static int q_c[];
    static int arr[];
    static int temp[];
	public static void main (String[] args) throws java.lang.Exception
	{
	    InputReader input = new InputReader(System.in);
	    OutputWriter out = new OutputWriter(System.out);
	    HashMap<Integer,Integer>map = new HashMap<>();
	    int n = input.readInt();
	    int k = input.readInt();
	    arr = new int[n];
	    long pre[] = new long[n];
	    for(int i =0;i<n;i++){
	        arr[i] = input.readInt();
	        if(i == 0)pre[i] = arr[i];
	        else pre[i] = pre[i-1]+arr[i];
	    }
	    double res =0;
	    for(int i =k-1;i<n;i++){
	        for(int j = 0;j<n && i+j<n;j++){
	            int l = i+j;
	            double sum = pre[l] - (j==0?0:pre[j-1]);
	            if(sum/(l-j+1)>res){
	                res = sum/(l-j+1);
	            }
	            
	        }
	    }
	    System.out.println(String.format("%.15f",res));
	    
	    

	}
}
 class InputReader{
		private InputStream stream;
		private byte[] buf = new byte[1024];
		private int curChar;
		private int numChars;
		private SpaceCharFilter filter;
		
		public InputReader(InputStream stream) {
			this.stream = stream;
		}
		
		public 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++];
		}
		
		public 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;
		}
		
		public String readString() {
			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 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;
		}
		
		public 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;
		}
		
		public boolean isSpaceChar(int c) {
			if (filter != null) {
				return filter.isSpaceChar(c);
			}
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}
		
		public String next() {
			return readString();
		}
		
		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	
 class OutputWriter {
		private final PrintWriter writer;
		
		public OutputWriter(OutputStream outputStream) {
			writer = new PrintWriter(new BufferedWriter(new OutputStreamWriter(outputStream)));
		}
		
		public OutputWriter(Writer writer) {
			this.writer = new PrintWriter(writer);
		}
		
		public void print(Object... objects) {
			for (int i = 0; i < objects.length; i++) {
				if (i != 0) {
					writer.print(' ');
				}
				writer.print(objects[i]);
			}
			writer.flush();
		}
		
		public void printLine(Object... objects) {
			print(objects);
			writer.println();
			writer.flush();
		}
		
		public void close() {
			writer.close();
		}
		
		public void flush() {
			writer.flush();
		}
	}
	   
//********************************************************************************************************************************
//////////////////////////////////NOTESSS//////////////////////////////////////////////////////////////////////
/*remember substring length you are dealing with take only those substrings
chain like pattern -> linked list (or) to from Arrays
finding degree can be done during input scanning itself(ok&=true:false flag trick)
longest subsquence can be solved in O(n) itself incase of consecutive numbers why try all subsequence go o dp[i-1]
(*******consecutive numberssssss*********)
initialize all global variables and collection ds
swapping changes the arr so make sure initialize with the original again(careful from where to start after swapping)
missing out character when comparing ==0 instead of =='0'
*/