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 java.util.*;
import java.awt.List;
import java.io.*;
import java.lang.*;
import java.lang.reflect.Array;

public class code3 {

	
	
	public static void main(String[] args) {
		InputReader in = new InputReader(System.in);
		PrintWriter pw = new PrintWriter(System.out);

		// Code starts..

		int n = in.nextInt();
		int k = in.nextInt();
		int[] a = new int[n+1];
		for(int i=0; i<n; i++)
		{
			a[i+1] = in.nextInt();
		}
		
		int[] dp = new int[n+1];
		for(int i=1; i<=n; i++)
			dp[i] = dp[i-1] + a[i];
		
		double ans = 0;
		for(int i=1; i<=n; i++)
		{
			for(int j=i+k-1; j<=n; j++)
			{
				
				double tmp = dp[j] - dp[i-1];
				//pw.println(tmp+" "+(j-i));
				tmp /= (double)(j-i+1);
				ans = Math.max(ans, tmp);
			}
		}
		
		
		pw.println(ans);
		
		
		
		
		
		// code ends...

		pw.flush();
		pw.close();
	}

	
	public static ArrayList<Integer>[] stree = new ArrayList[800005];
	public static int[] a;

		
	public static void build(int node, int start, int end)
	{
		
		
		if(start==end)
		{
			stree[node].add(a[start]);
			return;
		}
		
		int mid = (start+end)/2;
		build(2*node, start, mid);
		build(2*node+1, mid+1, end);
		
		/*int pos = 0;
	    for(int i=0;i<stree[2*node].size(); i++)
	    {
	        while(pos<stree[2*node+1].size() && stree[2*node+1].get(pos)<stree[2*node].get(i))
	        {
	            stree[node].add(stree[2*node+1].get(pos));
	            pos++;
	        }
	        stree[node].add(stree[2*node].get(i));
	    }
	    while(pos<stree[2*node+1].size())
	    {
	        stree[node].add(stree[2*node+1].get(pos));
	        pos++;
	    }
	    */
		
		for(int i: stree[2*node])
			stree[node].add(i);
		for(int i: stree[2*node+1])
			stree[node].add(i);
		
		
		Collections.sort(stree[node]);
		
		
		
		
		
		
	}
	
	
	public static int query(int node, int start, int end, int ll, int rl, int high)
	{
		
		if(ll>end || start>rl)
			return 0;
		
		if(ll<=start && end<=rl)
		{
		/*	int pos = -1;
		    int  l =0;
		    int r =stree[node].size()-1;

		     while(l<=r)
		        {
		          int mid=(l+r)/2;
		            if(stree[node].get(mid)<=high)
		            {
		                pos=mid;
		                l = mid+1;
		            }
		            else
		                r = mid-1;
		        }

		         
		     return pos+1;
		     */
			
			int i = Collections.binarySearch(stree[node], high);
			if (i < 0)
				i = -(i + 1);
			
			return i;
			
		     
			
		}
		
		
		int mid = (start+end)/2;
		int p1 = query(2*node, start, mid, ll, rl, high);
		int p2 = query(2*node+1, mid+1, end, ll, rl, high);
		
		return p1+p2;
		
	}

	
	
	public static long[][] mul(long[][] a, long[][] b){
		
		
		int n = a.length;
		int m = b[0].length;
		long[][] c = new long[n][m];
		
		for(int i=0; i<n; i++)
			for(int j=0; j<m; j++)
			{
				long tmp = 0;
				for(int k=0; k<a[0].length; k++)
					tmp =( (tmp+mod)%mod+(a[i][k]*b[k][j]+mod)%mod)%mod;
				c[i][j] = (tmp+mod)%mod;
			}
		
		return c;
	}
	
	
	
	public static long[][] pow(long[][] a,int  n)
	{
		
		long[][] res = a;
		while(n>0)
		{
			if(n%2==1)
			{
				res = mul(a, res);
			}
			
			a = mul(a, a);
			
			n/=2;
			
			
		}
		
		return res;
		
		
	}
	
	
	
	
	

	
	
	

	
	public static boolean isSubSequence(char[] str2, String str1) {

		int j = 0;
		int m = str1.length();
		int n = str2.length;

		for (int i = 0; i < n && j < m; i++)

			if (str1.charAt(j) == str2[i])

				j++;

		return (j == m);
	}

	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 c = 0;

	public static long mod = (long)Math.pow(10, 6)+3;
	public static int d;
	public static int p;
	public static int q;
	public static boolean flag;
	//public static long INF = Long.MAX_VALUE;

	public static void factSieve(int[] fact, long n) {

		for (int i = 2; i <= n; i += 2)
			fact[i] = 2;

		for (int i = 3; i <= n; i += 2) {
			if (fact[i] == 0) {
				fact[i] = i;

				for (int j = i; (long) j * i <= n; j++) {
					fact[(int) ((long) i * j)] = i;
				}
			}
		}

		/*
		 * int k = 1000; while(k!=1) { System.out.print(a[k]+" "); k /= a[k];
		 * 
		 * }
		 */
	}

	public static long floorsqrt(long n) {
		long ans = 0;
		long l = 0;
		long r = n;
		long mid = 0;
		while (l <= r) {
			mid = (l + r) / 2;
			if (mid * mid == n)
				return mid;

			if (mid * mid > n) {
				r = mid - 1;
			} else {
				ans = mid;
				l = mid + 1;
			}

		}

		return ans;
	}

	public static long fun(int[] a, int[] b, int m, int n) {
		long result = 0;
		for (int i = 0; i < m; i++)
			for (int j = 0; j < m; j++) {
				long[] fib = new long[Math.max(2, n + 2)];
				fib[1] = a[i];
				fib[2] = b[j];
				for (int k = 3; k <= n; k++)
					fib[k] = (fib[k - 1] % mod + fib[k - 2] % mod) % mod;
				result = (result % mod + fib[n] % mod) % mod;
			}

		return result;

	}

	/*
	 * public static double slope(pair p1, pair p2) { double m = INF; if((p1.x -
	 * p2.x)!=0) m = p1.y - p2.y/(p1.x - p2.x);
	 * 
	 * 
	 * return Math.abs(m);
	 * 
	 * }
	 */

	public static int count(String[] s, int f) {
		int count = 0;
		int n = s[0].length();

		if (f == 1) {
			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					if (i % 2 == 0) {
						if (j % 2 == 0 && s[i].charAt(j) == '0')
							count++;
						if (j % 2 == 1 && s[i].charAt(j) == '1')
							count++;
					}
					if (i % 2 == 1) {
						if (j % 2 == 1 && s[i].charAt(j) == '0')
							count++;
						if (j % 2 == 0 && s[i].charAt(j) == '1')
							count++;
					}

				}
			}
		} else {

			count = 0;

			for (int i = 0; i < n; i++) {
				for (int j = 0; j < n; j++) {
					if (i % 2 == 1) {
						if (j % 2 == 0 && s[i].charAt(j) == '0')
							count++;
						if (j % 2 == 1 && s[i].charAt(j) == '1')
							count++;
					}
					if (i % 2 == 0) {
						if (j % 2 == 1 && s[i].charAt(j) == '0')
							count++;
						if (j % 2 == 0 && s[i].charAt(j) == '1')
							count++;
					}

				}
			}

		}

		return count;

	}

	public static int gcd(int p2, int p22) {
		if (p2 == 0)
			return (int) p22;
		return gcd(p22 % p2, p2);
	}

	public static int findGCD(int arr[], int n) {
		int result = arr[0];
		for (int i = 1; i < n; i++)
			result = gcd(arr[i], result);

		return result;
	}

	public static void nextGreater(long[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] < a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] >= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}

	public static void nextGreaterRev(long[] a, int[] ans) {

		int n = a.length;
		int[] pans = new int[n];
		Arrays.fill(pans, -1);
		long[] arev = new long[n];
		for (int i = 0; i < n; i++)
			arev[i] = a[n - 1 - i];

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < n; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (arev[s] < arev[i]) {
					pans[s] = n - i - 1;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (arev[s] >= arev[i])
					stk.push(s);
			}

			stk.push(i);

		}

		// for(int i=0; i<n; i++)
		// System.out.print(pans[i]+" ");

		for (int i = 0; i < n; i++)
			ans[i] = pans[n - i - 1];

		return;

	}

	public static void nextSmaller(long[] a, int[] ans) {

		Stack<Integer> stk = new Stack<>();
		stk.push(0);

		for (int i = 1; i < a.length; i++) {

			if (!stk.isEmpty()) {
				int s = stk.pop();
				while (a[s] > a[i]) {
					ans[s] = i;
					if (!stk.isEmpty())
						s = stk.pop();
					else
						break;
				}
				if (a[s] <= a[i])
					stk.push(s);
			}

			stk.push(i);

		}
		return;

	}

	public static long lcm(int[] numbers) {
		long lcm = 1;
		int divisor = 2;
		while (true) {
			int cnt = 0;
			boolean divisible = false;
			for (int i = 0; i < numbers.length; i++) {
				if (numbers[i] == 0) {
					return 0;
				} else if (numbers[i] < 0) {
					numbers[i] = numbers[i] * (-1);
				}
				if (numbers[i] == 1) {
					cnt++;
				}
				if (numbers[i] % divisor == 0) {
					divisible = true;
					numbers[i] = numbers[i] / divisor;
				}
			}
			if (divisible) {
				lcm = lcm * divisor;
			} else {
				divisor++;
			}
			if (cnt == numbers.length) {
				return lcm;
			}
		}
	}

	public static long fact(long n) {

		long factorial = 1;
		for (int i = 1; i <= n; i++) {
			factorial *= i;
		}
		return factorial;
	}

	public static int lowerLimit(int[] a, int n) {
		int ans = 0;

		int ll = 0;
		int rl = a.length - 1;
		// System.out.println(a[rl]+" "+n);
		if (a[0] > n)
			return 0;
		if (a[0] == n)
			return 1;
		else if (a[rl] <= n)
			return rl + 1;

		while (ll <= rl) {

			int mid = (ll + rl) / 2;
			if (a[mid] == n) {
				ans = mid + 1;
				break;
			}

			else if (a[mid] > n) {
				rl = mid - 1;

			} else {
				ans = mid + 1;
				ll = mid + 1;
			}
		}

		return ans;
	}

	public static long choose(long total, long choose) {
		if (total < choose)
			return 0;
		if (choose == 0 || choose == total)
			return 1;
		return (choose(total - 1, choose - 1) + choose(total - 1, choose)) % mod;
	}

	public static int[] suffle(int[] a, Random gen) {
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}
		return a;
	}

	public static int floorSearch(int arr[], int low, int high, int x) {
		if (low > high)
			return -1;

		if (x > arr[high])
			return high;
		int mid = (low + high) / 2;

		if (mid > 0 && arr[mid - 1] < x && x < arr[mid])
			return mid - 1;

		if (x < arr[mid])
			return floorSearch(arr, low, mid - 1, x);

		return floorSearch(arr, mid + 1, high, x);
	}

	public static void swap(int a, int b) {
		int temp = a;
		a = b;
		b = temp;
	}

	public static ArrayList<Integer> primeFactorization(int n) {
		ArrayList<Integer> a = new ArrayList<Integer>();
		for (int i = 2; i * i <= n; i++) {
			while (n % i == 0) {
				a.add(i);
				n /= i;
			}
		}
		if (n != 1)
			a.add(n);
		return a;
	}
	
	
	

	public static void sieve(boolean[] isPrime, int n) {
		for (int i = 1; i < n; i++)
			isPrime[i] = true;

		isPrime[0] = false;
		isPrime[1] = false;

		for (int i = 2; i * i < n; i++) {
			if (isPrime[i] == true) {
				for (int j = (2 * i); j < n; j += i)
					isPrime[j] = false;
			}
		}
	}

	public static int lowerbound(ArrayList<Long> net, long c2) {
		int i = Collections.binarySearch(net, c2);
		if (i < 0)
			i = -(i + 2);
		return i;

	}
	
	public static int lowerboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 2);
		return i;

	}

	public static int uperbound(ArrayList<Integer> list, int c2) {
		int i = Collections.binarySearch(list, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static int uperboundArray(int[] dis, int c2) {
		int i = Arrays.binarySearch(dis, c2);
		if (i < 0)
			i = -(i + 1);
		return i;

	}

	public static long[] sort(long[] a) {
		Random gen = new Random();
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			long temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}

		Arrays.sort(a);
		return a;
	}

	public static int[] sort(int[] a) {
		Random gen = new Random();
		int n = a.length;
		for (int i = 0; i < n; i++) {
			int ind = gen.nextInt(n - i) + i;
			int temp = a[ind];
			a[ind] = a[i];
			a[i] = temp;
		}

		Arrays.sort(a);
		return a;
	}

	public static int GCD(int a, int b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static long GCD(long a, long b) {
		if (b == 0)
			return a;
		else
			return GCD(b, a % b);
	}

	public static void extendedEuclid(int A, int B) {
		if (B == 0) {
			d = A;
			p = 1;
			q = 0;
		} else {
			extendedEuclid(B, A % B);
			int temp = p;
			p = q;
			q = temp - (A / B) * q;
		}
	}

	public static long LCM(long a, long b) {
		return (a * b) / GCD(a, b);
	}

	public static int LCM(int a, int b) {
		return (a * b) / GCD(a, b);
	}

	public static int binaryExponentiation(int x, int n) {
		int result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = result * x;
			x = x * x;
			n = n / 2;
		}
		return result;
	}

	public static int[] countDer(int n) {
		int der[] = new int[n + 1];

		der[0] = 1;
		der[1] = 0;
		der[2] = 1;

		for (int i = 3; i <= n; ++i)
			der[i] = (i - 1) * (der[i - 1] + der[i - 2]);

		// Return result for n
		return der;
	}

	static long binomialCoeff(int n, int k) {
		long C[][] = new long[n + 1][k + 1];
		int i, j;

		// Calculate value of Binomial Coefficient in bottom up manner
		for (i = 0; i <= n; i++) {
			for (j = 0; j <= Math.min(i, k); j++) {
				// Base Cases
				if (j == 0 || j == i)
					C[i][j] = 1;

				// Calculate value using previosly stored values
				else
					C[i][j] = C[i - 1][j - 1] + C[i - 1][j];
			}
		}

		return C[n][k];
	}

	public static long binaryExponentiation(long x, long n) {
		long result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = result * x;
			x = (x % mod * x % mod) % mod;
			n = n / 2;
		}
		return result;
	}

	public static int modularExponentiation(int x, int n, int M) {
		int result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = (result * x) % M;
			x = (x * x) % M;
			n = n / 2;
		}
		return result;
	}

	public static long modularExponentiation(long x, long n, long M) {
		long result = 1;
		while (n > 0) {
			if (n % 2 == 1)
				result = (result * x) % M;
			x = (x * x) % M;
			n = n / 2;
		}
		return result;
	}

	public static int modInverse(int A, int M) {
		return modularExponentiation(A, M - 2, M);
	}

	public static long sie(long A, long M) {
		return modularExponentiation(A, M - 2, M);
	}

	public static boolean checkYear(int year) {
		if (year % 400 == 0)
			return true;

		if (year % 100 == 0)
			return false;

		if (year % 4 == 0)
			return true;
		return false;
	}

	public static boolean isPrime(int n) {

		if (n <= 1)
			return false;
		if (n <= 3)
			return true;

		if (n % 2 == 0 || n % 3 == 0)
			return false;

		for (int i = 5; i * i <= n; i = i + 6) {
			if (n % i == 0 || n % (i + 2) == 0)
				return false;
		}

		return true;
	}

	static class pair implements Comparable<pair>

	{
		Long x, y;

		pair(long x, long y) {
			this.x = x;
			this.y = y;
		}

		public int compareTo(pair o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);

			return result;
		}

		public String toString() {
			return x + " " + y;
		}

		public boolean equals(Object o) {
			if (o instanceof pair) {
				pair p = (pair) o;
				if(p.x-x==0 && p.y-y==0)
					return true;
				else
				return false;
			}
			return false;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode();
		}

	}
	

	static class triplet implements Comparable<triplet> {
		Integer x, y, z;

		triplet(int x, int y, int z) {
			this.x = x;
			this.y = y;
			this.z = z;
		}

		public int compareTo(triplet o) {
			int result = x.compareTo(o.x);
			if (result == 0)
				result = y.compareTo(o.y);
			if (result == 0)
				result = z.compareTo(o.z);

			return result;
		}

		public boolean equlas(Object o) {
			if (o instanceof triplet) {
				triplet p = (triplet) o;
				return x == p.x && y == p.y && z == p.z;
			}
			return false;
		}

		public String toString() {
			return x + " " + y + " " + z;
		}

		public int hashCode() {
			return new Long(x).hashCode() * 31 + new Long(y).hashCode() + new Long(z).hashCode();
		}
	}

	
	static class query implements Comparable<query> {
		Integer l,r, x, idx, tp;

	
		query(int l, int r, int x, int id, int tp)
		{
			this.l = l ;
			this.r = r;
			this.x = x;
			this.idx = id;
			this.tp = tp;
		}
		
		public int compareTo(query o) {
			int result = x.compareTo(o.x);
			
			return result;
		}

		
	

		
	}
	
	/*
	 * static class node implements Comparable<node>
	 * 
	 * { Integer x, y, z; node(int x,int y, int z) { this.x=x; this.y=y; this.z=z; }
	 * 
	 * public int compareTo(pair o) { int result = x.compareTo(o.x); if(result==0)
	 * result = y.compareTo(o.y); if(result==0) result = z.compareTo(z); return
	 * result; }
	 * 
	 * @Override public int compareTo(node o) { // TODO Auto-generated method stub
	 * return 0; } }
	 */
}