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.lang.*;
import java.lang.reflect.Array;
import java.math.*;

public class cf2 {
	 static class pair implements Comparable<pair>
		{
			Integer x,y;
			pair(int x,int y)
			{
				this.x=x;
				this.y=y;
			}
			public int compareTo(pair o) {
				if(y!=o.y)
					return y.compareTo(o.y);
				else
					return x.compareTo(o.x);
			}  
		}
	static long mod=1000000007;
	static boolean prime[];
	public static void main(String strings[])
	{
		InputReader in=new InputReader(System.in);
		PrintWriter pw=new PrintWriter(System.out);
		int n=in.nextInt();
		int k=in.nextInt();
		int[] arr=new int[n];
		for(int i=0;i<n;i++)
			arr[i]=in.nextInt();
		long[] sum=new long[n+1];
		sum[0]=0;
		for(int i=1;i<=n;i++)
			sum[i]=sum[i-1]+arr[i-1];
		double ans=0.0;
		int i=0;
		while(i+k-1<n)
		{
			ans=ans+sum[i+k]-sum[i];
			i++;
		}
		pw.print(ans/(n-k+1));
		pw.flush();
	}
	public static int distance(int x,int y,int p,int q)
	{
		int a=(x-p)*(x-p);
		int b=(y-q)*(y-q);
		int dis=a+b;
		return dis;
	}
	public static int bnum(int num)
	{
		int ans=0;
		for(int i=31;i>=0;i--)
		{
			if((num&(1<<i))!=0)
			{
				ans+=Math.pow(10,i);
			}
		}
		return ans;
	}
	public static int bsdown(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]<=item)
			{
				ans=mid;
				low=mid+1;
			}
			else
				high=mid-1;
				
		}
		return ans;
	}
	public static long inverse(long num)
	{
		return fastpow(num,mod-2,mod);
	}
	public static int bsupper(int a[],int item)
	{
		int low=0,high=a.length-1,ans=-1;
		while(low<=high)
		{
			int mid=low+(high-low)/2;
			if(a[mid]>=item)
			{
				ans=mid;
				high=mid-1;
			}
			else
				low=mid+1;
				
		}
		return ans;
	}	
	public static boolean isprime(int n)
	{
		for(int i=2;i*i<=n;i++)
		{
			if(n%i==0)
				return false;
		}
		return true;
	}
	public static long fact(long a,long mod)
	{
		long ans=1;
		for(int i=1;i<=a;i++)
		{
			ans*=i;
			ans%=mod;
		}
		return ans%mod;
		
	}
	public static long ncr(long n,long r,long mod)
	{
		long nom=1,dom=1;
		nom=(fact(n,mod))%mod;
		dom=(fact(r,mod)*fact(n-r,mod))%mod;
		return (nom*fastpow(dom,mod-2,mod))%mod;
	}
	public static long gcd(long x, long y)
	{
		if(x==0)
			return y;
		if(y==0)
			return x;
		long r=0, a, b;
		a = (x > y) ? x : y; // a is greater number
		b = (x < y) ? x : y; // b is smaller number
		r = b;
		while(a % b != 0)
		{
			r = a % b;
			a = b;
			b = r;
		}
		return r;
	}
	public static void prime(int n)
	{
		prime[0]=true;
		prime[1]=true;
		for(int i=2;i*i<=n;i++)
		{
			if(prime[i])
				continue;
			for(int j=i;j*i<=n;j++)
			{
				prime[i*j]=true;
			}
		}
	}
	static class InputReader {
		 
		private final InputStream stream;
		private final byte[] buf = new byte[8192];
		private int curChar, snumChars;
		private SpaceCharFilter filter;

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

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

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

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

		public int[] nextIntArray(int n) {
			int a[] = new int[n];
			for (int i = 0; i < n; i++) {
				a[i] = nextInt();
			}
			return a;
		}

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

		public String nextLine() {
			int c = snext();
			while (isSpaceChar(c))
				c = snext();
			StringBuilder res = new StringBuilder();
			do {
				res.appendCodePoint(c);
				c = snext();
			} while (!isEndOfLine(c));
			return res.toString();
		}

		public boolean isSpaceChar(int c) {
			if (filter != null)
				return filter.isSpaceChar(c);
			return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
		}

		private boolean isEndOfLine(int c) {
			return c == '\n' || c == '\r' || c == -1;
		}

		public interface SpaceCharFilter {
			public boolean isSpaceChar(int ch);
		}
	}
	public static long fastpow(long a,long b,long mod)
	{
		long ans=1;
		while(b!=0)
		{
			if(b%2==1)
			{
				ans=(ans*a)%mod;
			}
			a=(a*a)%mod;
			b/=2;
		}
		return ans;
	}
}