Problem: It's been almost a week since Polycarp couldn't get rid of insomnia. And as you may already know, one week in Berland lasts k days!

When Polycarp went to a doctor with his problem, the doctor asked him about his sleeping schedule (more specifically, the average amount of hours of sleep per week). Luckily, Polycarp kept records of sleep times for the last n days. So now he has a sequence a1, a2, ..., an, where ai is the sleep time on the i-th day.

The number of records is so large that Polycarp is unable to calculate the average value by himself. Thus he is asking you to help him with the calculations. To get the average Polycarp is going to consider k consecutive days as a week. So there will be n - k + 1 weeks to take into consideration. For example, if k = 2, n = 3 and a = [3, 4, 7], then the result is <image>.

You should write a program which will calculate average sleep times of Polycarp over all weeks.

Input

The first line contains two integer numbers n and k (1 ≤ k ≤ n ≤ 2·105).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

Output average sleeping time over all weeks. 

The answer is considered to be correct if its absolute or relative error does not exceed 10 - 6. In particular, it is enough to output real number with at least 6 digits after the decimal point.

Examples

Input

3 2
3 4 7


Output

9.0000000000


Input

1 1
10


Output

10.0000000000


Input

8 2
1 2 4 100000 123 456 789 1


Output

28964.2857142857

Note

In the third example there are n - k + 1 = 7 weeks, so the answer is sums of all weeks divided by 7.

Solution (in JAVA):

Solution:
import java.util.*;
import java.io.*;
import java.math.BigInteger;

public class Tester
{
	public static long mod=(long)(1e9+7);
	public static long xx,yy,d;
	static int minPrime[];
	static boolean isPrime[];
	
	public static void main(String[] args) throws IOException 
	{
		InputReader s=new InputReader(System.in);
        OutputStream outputStream = System.out;
        PrintWriter out=new PrintWriter(outputStream);
        
        /*long n = s.nextLong();
        String tmp = "";
        tmp = tmp + n;
        
        long dig = tmp.length();
        long mul = exp(10L, dig-1);
        
        if(dig == 1)
        {
        	out.println("1");
        	out.close();
        	return;
        }
        
        if(n % mul == 0)
        {
        	out.println(mul);
        }
        else
        {
        	int f = (int)tmp.charAt(0) - 48;
        	long year = (f+1)*mul;
        	out.println(year-n);
        }*/
        
        int n = s.nextInt();
        int k = s.nextInt();
        
        long a[] = new long[n];
        
        for(int i=0; i<n; i++)
        	a[i] = s.nextLong();
        
        long prefix[] = new long[n];
        prefix[0] = a[0];
        
        for(int i=1; i<n; i++)
        	prefix[i] = prefix[i-1] + a[i];
        
        long sum = 0;
        for(int i=0; i<=n-k; i++)
        {
        	if(i == 0)
        	{
        		sum += prefix[k-1];
        	}
        	else
        	{
        		sum += (prefix[i+k-1] - prefix[i-1]);
        	}
        }
        
        double ans = (double)sum/(n-k+1);
        out.println(ans);		
        
        
        out.close();
	}  
	
	static void modifiedSieve(int n)
	{
		minPrime = new int[n+1];
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(minPrime[i] == 0)
			{
				for(int j=i*i; j<=n; j=j+i)
				{
					if(minPrime[j] == 0)
						minPrime[j] = i;
				}
			}
		}
		
		for(int i=2; i<=n; i++)
		{
			if(minPrime[i] == 0)
				minPrime[i] = i;
		}
		
	}
	
	static void Sieve(int n)
	{
		isPrime = new boolean[n+1];
		Arrays.fill(isPrime, true);
		
		isPrime[0]=false;
		isPrime[1]=false;
		
		for(int i=2; i<=Math.sqrt(n); i++)
		{
			if(isPrime[i])
			{
				for(int j=i*i; j<=n; j=j+i)
					isPrime[j]=false;
			}
		}
		
	}
	
	static void extendedEuclid(long A, long B)
	{
		if(B == 0) {
	        d = A;
	        xx = 1;
	        yy = 0;
	    }
	    else {
	        extendedEuclid(B, A%B);
	        long temp = xx;
	        xx = yy;
	        yy = temp - (A/B)*yy;
	    }
	}
	
	static long gcd(long a,long b)
	{
		if(b==0)
			return a;
		
		return gcd(b,a%b);
	}
	
	static long modulo(long x,long y,long p)	
	{
		 long res = 1;
		 x = x % p;  
		 
	    while (y > 0)
	    {
	        if (y%2==1)
	            res = (res*x) % p;
	 
	        y = y>>1;
	        x = (x*x) % p;  
	    }
	    return res;
	}
	
	public static int firstOccurence(int a[], int key)
	{
		int low = 0;
		int high = a.length-1;
		
		while(low <= high)
		{
			int mid = low + (high - low)/2;
			
			if(key <= a[mid])
			{
				high = mid - 1;
			}
			else if(key > mid)
			{
				low = mid + 1;
			}
		}
		
		return low;
	}
	
	public static int lastOccurence(int a[], int key)
	{
		int low = 0;
		int high = a.length-1;
		
		while(low <= high)
		{
			int mid = low + (high - low)/2;
			
			if(key >= a[mid])
			{
				low = mid + 1;
			}
			else if(key < a[mid])
			{
				high = mid - 1;
			}
		}
		
		return high;
	}
	
	public static void debug(Object... o)
	{
		System.out.println(Arrays.deepToString(o));
	}
	
	static long exp(long a, long b)
	{
		if(b==0)
			return 1;
		if(b==1)
			return a;
		if(b==2)
			return a*a;

		if(b%2==0)
			return exp(exp(a,b/2),2);
		else
			return a*exp(exp(a,(b-1)/2),2);
	}

	static class Pair implements Comparable<Pair>
	{
		long x,y;
		Pair(long ii, long cc)
		{
			x=ii;
			y=cc;
		}
		
		public int compareTo(Pair o) 
		{
			if(Long.compare(this.x, o.x) != 0)
				return Long.compare(this.x, o.x);
			else
				return Long.compare(this.y, o.y);
		}
		
		public int hashCode() {
			int hu = (int) (x ^ (x >>> 32));
			int hv = (int) (y ^ (y >>> 32));
			return 31 * hu + hv;
		}
 
		public boolean equals(Object o) {
			Pair other = (Pair) o;
			return x == other.x && y == other.y;
		}
		
		public String toString() {
			return "[x=" + x + ", y=" + y + "]";
		}
		
	}

    static final class InputReader{
        private final InputStream stream;
        private final byte[] buf=new byte[1024];
        private int curChar;
        private int Chars;
        public InputReader(InputStream stream){this.stream=stream;}
        private int read()throws IOException{
            if(curChar>=Chars){
                curChar=0;
                Chars=stream.read(buf);
                if(Chars<=0)
                    return -1;
            }
            return buf[curChar++];
        }
        public final int nextInt()throws IOException{return (int)nextLong();}
        public final long nextLong()throws IOException{
            int c=read();
            while(isSpaceChar(c)){
                c=read();
                if(c==-1) throw new IOException();
            }
            boolean negative=false;
            if(c=='-'){
                negative=true;
                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 negative?(-res):(res);
        }
        public final int[] nextIntBrray(int size)throws IOException{
            int[] arr=new int[size];
            for(int i=0;i<size;i++)arr[i]=nextInt();
            return arr;
        }
        public final String nextString()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(!isSpaceChar(c));
            return res.toString();
        }
        public final String nextLine()throws IOException{
            int c=read();
            while(isSpaceChar(c))c=read();
            StringBuilder res=new StringBuilder();
            do{
                res.append((char)c);
                c=read();
            }while(c!='\n' && c!=-1);
            return res.toString();
        }
        private boolean isSpaceChar(int c)
        {
            return c==' '||c=='\n'||c=='\r'||c=='\t'||c==-1;
        }
    }
 
}