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.io.BufferedReader;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.InputMismatchException;
import java.util.Iterator;
import java.util.LinkedList;
import java.util.Queue;
import java.util.TreeMap;
import java.util.TreeSet;

											public class Solution1 implements Runnable
											{
												static final long MAX = 464897L;
												static class InputReader
												{
													private InputStream stream;
													private byte[] buf = new byte[1024];
													private int curChar;
													private int numChars;
													private SpaceCharFilter filter;
													private BufferedReader br=new BufferedReader(new InputStreamReader(System.in));
											 
													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 String nextLine()
													{
														String str = "";
											            try
											            {
											                str = br.readLine();
											            }
											            catch (IOException e)
											            {
											                e.printStackTrace();
											            }
											            return str;
													}
													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 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 double nextDouble() 
													{
														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, nextInt());
															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, nextInt());
																if (c < '0' || c > '9')
																	throw new InputMismatchException();
																m /= 10;
																res += (c - '0') * m;
																c = read();
															}
														}
														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 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);
													}
												}
											 	
												public static void main(String args[]) throws Exception
												{
													new Thread(null, new Solution1(),"Solution",1<<26).start();
												}	
												public static int gcd(int a, int b)
											    {
											        if (a == 0)
											            return b;
											         
											        return gcd(b%a, a);
											    }
												int lcm(int a, int b)
												{
												    return (a*b)/gcd(a, b);
												}
												ArrayList<Integer> adj[];
												static long MOD = 1000000007;
												boolean[][] visited;
												int[] dx = {1,-1,0,0};
												int[] dy = {0,0,1,-1};
												public void run() 
												{
													InputReader sc= new InputReader(System.in);
													PrintWriter w= new PrintWriter(System.out);
													int n = sc.nextInt();
													int m = sc.nextInt();
													int[] arr = new int[n];
													long[] prefix=  new long[n];
													for(int i = 0;i < n;i++) {
														arr[i] = sc.nextInt();
														if(i == 0) {
															prefix[i] = arr[i];
															continue;
														}
														prefix[i] = prefix[i-1] + arr[i];
													}
													long ans = 0;
													int cnt = 0;
													for(int i = 0;i < n;i++) {
														if(i + m - 1 < n) {
															cnt++;
															if(i == 0) {
																ans += prefix[i+m - 1];
																continue;
															}
															ans += prefix[i + m - 1] - prefix[i-1];
														
														}else {
															break;
														}
													}
													System.out.printf("%.10f",(ans * 1.0)/cnt);
													w.close();
												}
												int build(int n) {
													int ans = 1;
													for(int i = 0;i < n;i++) {
														ans = ans * 10;
													}
													return ans;
												}
												int digit(int n) {
													int ans=  0;
													while(n != 0) {
														n = n/10;
														ans++;
													}
													return ans;
												}
												boolean fun(int[] arr,int mid,int val) {
													int count = 0;
													for(int i = 0;i < arr.length;i++) {
														if(arr[i] <= count) {
															count++;
														}else if(mid > 0) {
															count++;
															mid--;
														}
													}
													if(count >=	val) {
														return true;
													}
													return false;
												}
												void populate(char[][] ch,int n,int m,Queue<Pair> q,int d) {
													while(!q.isEmpty()) {
														Pair poll = q.poll();
														if(level[poll.a][poll.b] == d) {
															break;
														}
														for(int i = 0;i < 4;i++) {
															int x = poll.a;
															int y = poll.b;
															if(x + dx[i] >= 0 && x + dx[i] < n && y + dy[i] < m && y + dy[i] >= 0 && !visited[x+dx[i]][y+dy[i]]) {
																Pair y1 = new Pair(x + dx[i],y + dy[i]);
																q.add(y1);
																ch[x + dx[i]][y + dy[i]] = 'M';
																visited[x+dx[i]][y + dy[i]] = true;
																level[x+dx[i]][y+dy[i]] = level[x][y] + 1;
															}
														}
													}
												}
												int[][] level;
												int calc(char[][] ch,int n,int m,int x,int y,int one,int two) {
													if(ch[x][y] == 'M' || ch[one][two] == 'M') {
														return -1;
													}
													visited[x][y] = true;
													Queue<Pair> q = new LinkedList();
													Pair p = new Pair(x,y);
													q.add(p);
													int d = 0;
													level[x][y] = 0;
													while(!q.isEmpty()) {
														Pair poll = q.poll();
														if(level[one][two] != -1) {
															return level[one][two];
														}
														for(int i = 0;i < 4;i++) {
															x = poll.a;
															y = poll.b;
															if(x + dx[i] >= 0 && x + dx[i] < n && y + dy[i] < m && y + dy[i] >= 0 && !visited[x+dx[i]][y+dy[i]] && ch[x+dx[i]][y+dy[i]] != 'M') {
																Pair y1 = new Pair(x + dx[i],y + dy[i]);
																q.add(y1);
																visited[x+dx[i]][y + dy[i]] = true;
																level[x+dx[i]][y+dy[i]] = level[x][y] + 1;
															}
														}
														d++;
													}
													return level[one][two];
												}
											    static long power(long x, long y,long p)
												    {
												        // Initialize result
												        long res = 1;     
												        
												        // Update x if it is more  
												        // than or equal to p
												        x = x % p; 
												     
												        while (y > 0)
												        {
												            // If y is odd, multiply x
												            // with result
												            if((y & 1)==1)
												                res = (res * x) % p;
												     
												            // y must be even now
												            // y = y / 2
												            y = y >> 1; 
												            x = (x * x) % p; 
												        }
												        return res;
												    }
												static class Pair implements Comparable<Pair>{
													int a;
													int b;
													Pair(int a,int b){
														this.a  =a;
														this.b = b;
													}
													Pair(){}	
													public boolean equals(Object o)
													{
														Pair p = (Pair)o;
														
														return true;
													}
													
													public int compareTo(Pair p){
														return Integer.compare(a,b);
													}
												
												}
												
								}