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.*;
import java.math.*;
import java.security.KeyStore.Entry;
import java.util.*;
	
		
		
		
		
			public class Q2 {
				
				static long MOD = 1000000007;
				static boolean b[], b1[], check;
				static ArrayList<Integer>[] amp, pa;
				static ArrayList<Pair>[] amp1;
				static ArrayList<Pair>[][] damp;
				static int left[],right[],end[],sum[],dist[],cnt[],start[],color[],parent[],prime[],size[];
				static long ans = 0,k;
				static int p = 0;
				static FasterScanner sc = new FasterScanner(System.in);
				static Queue<Integer> q = new LinkedList<>();
				static BufferedWriter log;
				static HashSet<Pair> hs;
				static HashMap<Pair,Integer> hm;
				static PriorityQueue<Integer> pri[];
				static ArrayList<Integer>[] level;
				static Stack<Integer> st;
				static boolean boo[][];
				static Pair prr[];
				static long parent1[],parent2[],size1[],size2[],arr1[],SUM[],lev[], fibo[];
				static int arr[], ver[][];
				public static void main(String[] args) throws Exception {
			    	/*new Thread(null, new Runnable() {
						public void run() {
							try {
		
						} catch (Exception e) {
								System.out.println(e);
							}
						}
					}, "1", 1 << 26).start();*/
					soln();
				}
				private static boolean oj = System.getProperty("ONLINE_JUDGE") != null;
				private static void tr(Object... o) {
					if (!oj)
						System.out.println(Arrays.deepToString(o));
				}
				static long dp[][];
				static int N,K,T,A,B;
				static int time;
				static int cost[][];
				static boolean b11[];
				static HashMap<Integer,Integer> h = new HashMap<>();
				static HashSet<Pair> chec;
				static long ans1;		static long ans2;
				static int BLOCK, MAX = 10000000, door[][];
				static double pi = Math.PI;
				static int Arr[], Brr[], pow[],  M;
				static long fact[] = new long[100000+1];
				static HashMap<Pair,Integer> hm1;
				static HashSet<Integer> hs1[], hs2[];
				static PriorityQueue<Integer> pq = new PriorityQueue<>(Collections.reverseOrder());
				static int phi[];
				public static void soln() throws IOException {
					//FasterScanner in = new FasterScanner(new FileInputStream("C:\\Users\\Admin\\Desktop\\input50.txt"));
					//FasterScanner sc = new FasterScanner(new FileInputStream("C:\\Users\\Admin\\Desktop\\input.txt"));
					//PrintWriter log = new PrintWriter("C:\\Users\\Admin\\Desktop\\output.txt");
					//long s = System.currentTimeMillis();
					log = new BufferedWriter(new OutputStreamWriter(System.out));
					int n = sc.nextInt(), k = sc.nextInt();
					int arr[] = sc.nextIntArray(n);
					double ans = 0;
					long ps[] = new long[n+1];
					for(int i = 0;i<n;i++){
						ps[i+1] = ps[i]+arr[i];
					}
					for(int i = 0; i<= n-k;i++){
						ans += (ps[i+k]-ps[i]);
					}
					System.out.println(ans/(n-k+1));
					//out.close();
					//tr(System.currentTimeMillis() - s + "ms");
					log.close();
					//out.close();
				}
				static long recur(int x, long k, int m){
					if(k==0) return 1;
					if(m==1) return 0;
					return power(x, recur(x,k-1,phi[m]), m);
				}
				static void bfs(){
					while(!q.isEmpty()){
						int y = q.poll();
						for(int x:amp[y]){
							b1[x] = true;
							if(door[x][0]==y){
								int d = door[x][1];
								if(b[d]){
									if(prime[d]!=(1-arr[x-1]^prime[y])){
										check = true;
										return;
									}
								}
								else{
									prime[d] = 1-arr[x-1]^prime[y];
									q.add(d);
									b[d] = true;
								}
							}
							else{
								int d = door[x][0];
								if(b[d]){
									if(prime[d]!=(1-arr[x-1]^prime[y])){
										check = true;
										return;
									}
								}
								else{
									prime[d] = 1-arr[x-1]^prime[y];
									q.add(d);
									b[d] = true;
								}
							}
						}
					}
				}
				public static class FenwickTree {
					
				    int[] array; // 1-indexed array, In this array We save cumulative information to perform efficient range queries and updates
	
				    public FenwickTree(int size) {
				        array = new int[size + 1];
				    }
				    public int rsq(int ind) {
				        assert ind > 0;
				        int sum = 0;
				        while (ind > 0) {
				            sum += array[ind];
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and decrementing ind by that number
				            ind -= ind & (-ind);
				        }
				        return sum;
				    }
				    public int rsq(int a, int b) {
				        assert b >= a && a > 0 && b > 0;
				        return rsq(b) - rsq(a - 1);
				    }
				    public void update(int ind, int value) {
				        assert ind > 0;
				        while (ind < array.length) {
				            array[ind] += value;
				            //Extracting the portion up to the first significant one of the binary representation of 'ind' and incrementing ind by that number
				            ind += ind & (-ind);
				        }
				    }
	
				    public int size() {
				        return array.length - 1;
				    }
				}
				static double power(double x, long y)
				{
				    if (y == 0)
				        return 1;
				    double p = power(x, y/2);
				    p = (p * p);
				 
				    return (y%2 == 0)? p : (x * p);
				}
				static void Bfs(int x){
					q.add(x);
					b[x] = true;
					while(!q.isEmpty()){
						int y = q.poll();
						b[y] = true;
						for(int p:hs2[y]){
							if(!b[p]){
								if(!hs1[y].contains(p)) dist[p] = dist[y]-1;
								else dist[p] = dist[y]+1;
								q.add(p);
							}
						}
					}
				}
				static int Dfs(int x, int val){
					b[x] = true;
					for(int p:hs2[x]){
						if(!b[p]){
							if(!hs1[x].contains(p)) val++;
							val += Dfs(p,0);
						}
					}
					return val;
				}
				static long nCr(int n, int r){
					if(n<r) return 0;
					else return (((fact[n]*modInverse(fact[r], MOD))%MOD)*modInverse(fact[n-r], MOD))%MOD;
				}
				static void dfs1(int x, int p){
					arr1[x] += lev[x];
					for(int v:amp[x]){
						if(v!=p){
							dfs1(v,x);
						}
					}
				}
				static void dfs(int x, int p){
					start[x] = time++;
					for(int v:amp[x]){
						if(v!=p){
							dfs(v,x);
						}
					}
					end[x] = time;
				}
				
				
				static void bfs(int x){
					
				}
				public static void seive(int n){
					b = new boolean[(n+1)];
					Arrays.fill(b, true);
					b[1] = true;
					for(int i = 2;i*i<=n;i++){
						if(b[i]){
							for(int p = 2*i;p<=n;p+=i){
								b[p] = false;
							}
						}
					}
					/*for(int i = 2;i<=n;i++){
						if(b[i]) prime[i] = i;
					}*/
				}
				
				static class Graph{
					int vertex;
					int weight;
					Graph(int v, int w){
						vertex = v;
						weight = w;
					}
				}
				static class Pair implements Comparable<Pair> {
					int u;
					int v;
					double ans;
					public Pair(){
						u = 0;
						v = 0;
					}
					public Pair(int u, int v) {
						this.u = u;
						this.v = v;
					}
					public int hashCode() {
						return Objects.hash();
					}
					public boolean equals(Object o) {
						Pair other = (Pair) o;
						return ((u == other.u && v == other.v));
					}
			 
					public int compareTo(Pair other) {
						//return Double.compare(ans, other.ans);
						return Long.compare(u, other.u);// != 0 ? (Long.compare(u, other.u)) : (Long.compare(v,other.v));
					}
					
					public String toString() {
						return "[u=" + u + ", v=" + v + "]";
					}
				}
				
				public static void buildGraph(int n){
					for(int i =0;i<n;i++){
						int x = sc.nextInt()-1, y = sc.nextInt()-1;
						//hm.put(new Pair(x,y), i+1);
						hs1[x].add(y);
						hs2[y].add(x);
						hs2[x].add(y);
					}
				}
				
				
				public static int getParent(long x){
					while(parent[(int) x]!=x){
						parent[ (int) x] = parent[(int) parent[ (int) x]];
						x = parent[ (int) x];
					}
					return (int) x;
				}
				static long min(long a, long b, long c){
					if(a<b && a<c) return a;
					if(b<c) return b;
					return c;
				}
				/*
				
				static class Pair3{
					int x, y ,z;
					Pair3(int x, int y, int z){
						this.x = x;
						this.y = y;
						this.z = z;
					}
				}*/
				 static void KMPSearch(String pat, String txt)
				    {
				        int M = pat.length();
				        int N = txt.length();
				 
				        // create lps[] that will hold the longest
				        // prefix suffix values for pattern
				        int lps[] = new int[M];
				        int j = 0;  // index for pat[]
				 
				        // Preprocess the pattern (calculate lps[]
				        // array)
				        computeLPSArray(pat,M,lps);
				 
				        int i = 0;  // index for txt[]
				        while (i < N)
				        {
				            if (pat.charAt(j) == txt.charAt(i))
				            {
				                j++;
				                i++;
				            }
				            if (j == M)
				            {
				               // parent.add((i-j));
				                j = lps[j-1];
				            }
				 
				            // mismatch after j matches
				            else if (i < N && pat.charAt(j) != txt.charAt(i))
				            {
				                // Do not match lps[0..lps[j-1]] characters,
				                // they will match anyway
				                if (j != 0)
				                    j = lps[j-1];
				                else
				                    i = i+1;
				            }
				        }
				    }
				 static void computeLPSArray(String pat, int M, int lps[])
				    {
				        // length of the previous longest prefix suffix
				        int len = 0;
				        int i = 1;
				        lps[0] = 0;  // lps[0] is always 0
				 
				        // the loop calculates lps[i] for i = 1 to M-1
				        while (i < M)
				        {
				            if (pat.charAt(i) == pat.charAt(len))
				            {
				                len++;
				                lps[i] = len;
				                i++;
				            }
				            else  // (pat[i] != pat[len])
				            {
				                // This is tricky. Consider the example.
				                // AAACAAAA and i = 7. The idea is similar 
				                // to search step.
				                if (len != 0)
				                {
				                    len = lps[len-1];
				 
				                    // Also, note that we do not increment
				                    // i here
				                }
				                else  // if (len == 0)
				                {
				                    lps[i] = len;
				                    i++;
				                }
				            }
				        }
				    }
				private static void permutation(String prefix, String str) {
				    int n = str.length();
				    if (n == 0); //hs.add(prefix);
				    else {
				        for (int i = 0; i < n; i++)
				            permutation(prefix + str.charAt(i), str.substring(0, i) + str.substring(i+1, n));
				    }
				}
				
				public static void buildTree(int n){
					int arr[] = sc.nextIntArray(n);
					for(int i = 0;i<n;i++){
						int x = arr[i]-1;
						amp[i+1].add(x);
						amp[x].add(i+1);
					}
				}
				
				static class SegmentTree {
					boolean st[];
					boolean lazy[];
		
					SegmentTree(int n) {
						int size = 4 * n;
						st = new boolean[size];
						Arrays.fill(st, true);
						lazy = new boolean[size];
						Arrays.fill(lazy, true);
						//build(0, n - 1, 1);
					}
					
					/*long[] build(int ss, int se, int si) {
						if (ss == se) {
							st[si][0] = 1;
							st[si][1] = 1;
							st[si][2] = 1;
							return st[si];
						}
						int mid = (ss + se) / 2;
						long a1[] = build(ss, mid, si * 2), a2[] = build(mid + 1, se,
								si * 2 + 1);
						long ans[] = new long[3];
						if (arr[mid] < arr[mid + 1]) {
							ans[1] = Math.max(a2[1], Math.max(a1[1], a1[2] + a2[0]));
							if (a1[1] == (mid - ss + 1))
								ans[0] = ans[1];
							else
								ans[0] = a1[0];
							if (a2[2] == (se - mid))
								ans[2] = ans[1];
							else
								ans[2] = a2[2];
						} else {
							ans[1] = Math.max(a1[1], a2[1]);
							ans[0] = a1[0];
							ans[2] = a2[2];
						}
						st[si] = ans;
						return st[si];
					}*/
		
					void update(int si, int ss, int se, int idx, long x) {
						if (ss == se) {
							//arr[idx] += val;
							st[si]=false;
						} 
						else {
							int mid = (ss + se) / 2;
							if(ss <= idx && idx <= mid)
					        {
					             update(2*si, ss, mid, idx, x);
					        }
					        else
					        { update(2*si+1, mid+1, se, idx, x);
					        }
							st[si] = st[2*si]|st[2*si+1];
						}
					}
					/*boolean get(int qs, int qe, int ss, int se, int si){
						if(qs>se || qe<ss) return 0;
						if (qs <= ss && qe >= se) {
							return st[si];
						}
						int mid = (ss+se)/2;
						return get(qs, qe, ss, mid, si * 2)+get(qs, qe, mid + 1, se, si * 2 + 1);
					}*/
					void updateRange(int node, int start, int end, int l, int r, boolean val)
					{
					    if(!lazy[node])
					    { 
					        // This node needs to be updated
					        st[node] = lazy[node];    // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];                  // Mark child as lazy
					            lazy[node*2+1] = lazy[node];                // Mark child as lazy
					        }
					        lazy[node] = true;                                  // Reset it
					    }
					    if(start > end || start > r || end < l)              // Current segment is not within range [l, r]
					        return;
					    if(start >= l && end <= r)
					    {
					        // Segment is fully within range
					        st[node] =  val;
					        if(start != end)
					        {
					            // Not leaf node
					            lazy[node*2] = val;
					            lazy[node*2+1] = val;
					        }
					        return;
					    }
					    int mid = (start + end) / 2;
					    updateRange(node*2, start, mid, l, r, val);        // Updating left child
					    updateRange(node*2 + 1, mid + 1, end, l, r, val);   // Updating right child
					    st[node] = st[node*2] | st[node*2+1];        // Updating root with max value 
					}
		
					boolean queryRange(int node, int start, int end, int l, int r)
					{
					    if(start > end || start > r || end < l)
					        return false;         // Out of range
					    if(!lazy[node])
					    {
					        // This node needs to be updated
					        st[node] = lazy[node];            // Update it
					        if(start != end)
					        {
					            lazy[node*2] = lazy[node];         // Mark child as lazy
					            lazy[node*2+1] = lazy[node];    // Mark child as lazy
					        }
					        lazy[node] = true;                 // Reset it
					    }
					    if(start >= l && end <= r)             // Current segment is totally within range [l, r]
					        return  st[node];
					    int mid = (start + end) / 2;
					    boolean p1 = queryRange(node*2, start, mid, l, r);         // Query left child
					    boolean b = queryRange(node*2 + 1, mid + 1, end, l, r); // Query right child
					    return (p1 | b);
					}
					void print() {
						for (int i = 0; i < st.length; i++) {
							System.out.print(st[i]+" ");
						}
						System.out.println();
					}
				}
				static int convert(int x){
					int cnt = 0;
					String str = Integer.toBinaryString(x);
					//System.out.println(str);
					for(int i = 0;i<str.length();i++){
						if(str.charAt(i)=='1'){
							cnt++;
						}
					}
					int ans = (int) Math.pow(3, 6-cnt);
					return ans;
				}
				static class Node2{
					Node2 left = null;
					Node2 right = null;
					Node2 parent = null;
					int data;
				}
				static class BinarySearchTree{
					Node2 root = null;
					int height = 0;
					int max = 0;
					int cnt = 1;
					ArrayList<Integer> parent = new ArrayList<>();
					HashMap<Integer, Integer> hm = new HashMap<>();
					public void insert(int x){
						Node2 n = new Node2();
						n.data = x;
						if(root==null){
							root = n;
						}
						else{
							Node2 temp = root,temb = null;
							while(temp!=null){
								temb = temp;
								if(x>temp.data) temp = temp.right;
								else temp = temp.left;
							}
							if(x>temb.data) temb.right = n;
							else temb.left = n;
							n.parent = temb;
							parent.add(temb.data);
						}
					}
					public Node2 getSomething(int x, int y, Node2 n){
						if(n.data==x || n.data==y) return n;
						else if(n.data>x && n.data<y) return n;
						else if(n.data<x && n.data<y) return getSomething(x,y,n.right);
						else return getSomething(x,y,n.left);
					}
					public Node2 search(int x,Node2 n){
						if(x==n.data){
							max = Math.max(max, n.data);
							return n;
						}
						if(x>n.data){
							max = Math.max(max, n.data);
							return search(x,n.right);
						}
						else{
							max = Math.max(max, n.data);
							return search(x,n.left);
						}
					}
					public int getHeight(Node2 n){
						if(n==null) return 0;
						height = 1+ Math.max(getHeight(n.left), getHeight(n.right));
						return height;
					}
				}
				static long findDiff(long[] arr, long[] brr, int m){
					int i = 0, j = 0;
					long fa = 1000000000000L;
					while(i<m && j<m){
						long x = arr[i]-brr[j];
						if(x>=0){
							if(x<fa) fa = x;
							j++;
						}
						else{
							if((-x)<fa) fa = -x;
							i++;
						}
					}
					return fa;
				}
				public static long max(long x, long y, long z){
					if(x>=y && x>=z) return x;
					if(y>=x && y>=z) return y;
					return z;
				}
				
				static long modInverse(long a, long mOD2){
				            return  power(a, mOD2-2, mOD2);
				}
				static long power(long x, long y, long m)
				{
				    if (y == 0)
				        return 1;
				    long p = power(x, y/2, m) % m;
				    p = (p * p) % m;
				 
				    return (y%2 == 0)? p : (x * p) % m;
				}
				static long d,x,y;
				public static void extendedEuclidian(long a, long b){
					if(b == 0) {
				        d = a;
				        x = 1;
				        y = 0;
				    }
				    else {
				        extendedEuclidian(b, a%b);
				        int temp = (int) x;
				        x = y;
				        y = temp - (a/b)*y;
				    }
				}
				
				public static long gcd(long n, long m){
					if(m!=0) return gcd(m,n%m);
					else return n;
				}
				
				static BufferedReader reader;
			    static StringTokenizer tokenizer;
			    static PrintWriter writer;
			
			
			   
			    static class FasterScanner {
		
					private final InputStream stream;
					private final byte[] buf = new byte[8192];
					private int curChar, snumChars;
					private SpaceCharFilter filter;
		
					public FasterScanner(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 long[] nextLongArray(int n) {
						long a[] = new long[n];
						for (int i = 0; i < n; i++) {
							a[i] = nextLong();
						}
						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);
					}
				}
			}