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 com.sun.corba.se.impl.orbutil.ORBConstants;
import java.io.PrintWriter;

import java.util.*;
import java.util.Arrays ; 

 
import java.io.DataInputStream; 
import java.io.FileInputStream; 
import java.io.IOException; 
import java.lang.reflect.Array;


public class Test{
     static PrintWriter  pw = new PrintWriter(System.out); 
static class Reader 
    { 
    
        final private int BUFFER_SIZE = 1 << 16; 
        private DataInputStream din; 
        private byte[] buffer; 
        private int bufferPointer, bytesRead; 
  
        public Reader() 
        { 
            din = new DataInputStream(System.in); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public Reader(String file_name) throws IOException 
        { 
            din = new DataInputStream(new FileInputStream(file_name)); 
            buffer = new byte[BUFFER_SIZE]; 
            bufferPointer = bytesRead = 0; 
        } 
  
        public String readLine() throws IOException 
        { 
            byte[] buf = new byte[64]; // line length 
            int cnt = 0, c; 
            while ((c = read()) != -1) 
            { 
                if (c == '\n') 
                    break; 
                buf[cnt++] = (byte) c; 
            } 
            return new String(buf, 0, cnt); 
        } 
  
        public int nextInt() throws IOException 
        { 
            int ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do
            { 
                ret = ret * 10 + c - '0'; 
            }  while ((c = read()) >= '0' && c <= '9'); 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public long nextLong() throws IOException 
        { 
            long ret = 0; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        public double nextDouble() throws IOException 
        { 
            double ret = 0, div = 1; 
            byte c = read(); 
            while (c <= ' ') 
                c = read(); 
            boolean neg = (c == '-'); 
            if (neg) 
                c = read(); 
  
            do { 
                ret = ret * 10 + c - '0'; 
            } 
            while ((c = read()) >= '0' && c <= '9'); 
  
            if (c == '.') 
            { 
                while ((c = read()) >= '0' && c <= '9') 
                { 
                    ret += (c - '0') / (div *= 10); 
                } 
            } 
  
            if (neg) 
                return -ret; 
            return ret; 
        } 
  
        private void fillBuffer() throws IOException 
        { 
            bytesRead = din.read(buffer, bufferPointer = 0, BUFFER_SIZE); 
            if (bytesRead == -1) 
                buffer[0] = -1; 
        } 
  
        private byte read() throws IOException 
        { 
            if (bufferPointer == bytesRead) 
                fillBuffer(); 
            return buffer[bufferPointer++]; 
        } 
  
        public void close() throws IOException 
        { 
            if (din == null) 
                return; 
            din.close(); 
        } 
    } 
   

static int find(long x[],long r){
    int sum =0 ;
    
    for (int i = 0; i < x.length; i++) {
        if(x[i]==r) return i+1 ;
    }
    return sum ;
}
static int [] find2(int x[][],int temp,int y[]){
    for (int i = 0; i < x.length; i++) {
        int sum=0 ;
        for (int j = 0; j < x.length; j++) {
           sum+=x[j][i] ;
        }
        y[i]=sum ;
   
    }
   return y;
    
}
static void found(LinkedList<Integer> l1,String s,LinkedList<Integer> l2){
    for (int i = 0; i < s.length()-1; i++) {
        String temp ="" ;
                temp +=(char)s.charAt(i);
                temp +=(char)s.charAt(i+1);
        if(temp.equals("AB"))l1.add(i) ;
        if(temp.equals("BA"))l2.add(i) ;
    }
}
 static String db(String s){
     StringBuilder b= new StringBuilder(s) ;
     
     return s+(b.reverse().toString()) ; 
    
 }
 static String btw(String s,char c){
     StringBuilder b= new StringBuilder(s) ;
     
     return (s+c)+(b.reverse().toString()) ; 
    
 }

      
      
            


    public static void main(String[] args) throws IOException  {

    
        
   Reader  in =new Reader ();
 // Scanner  in =new Scanner (System.in);
  int  n=in.nextInt(), q=in.nextInt() ;
   double x[]=new double [n+1] ; 
    //long long sum = 0 ;
    for(int i=1;i<=n;i++)
        x[i]=in.nextInt() ; 
    for(int i=1;i<=n;i++)
    x[i]+=x[i-1] ;

   // vector <double> v;
   double max =0.0 ; 
    for(int i=1;i<=n-q+1;i++){
     for(int j=i+q-1;j<=n;j++){
       max =Math.max(((x[j]-x[i-1])/(j-i+1)),max) ;
     }
    }
     pw.println(max) ; 

        pw.close();
}
}