Problem:
Score : 400 points

Problem Statement

We have N dice arranged in a line from left to right. The i-th die from the left shows p_i numbers from 1 to p_i with equal probability when thrown.

We will choose K adjacent dice, throw each of them independently, and compute the sum of the numbers shown. Find the maximum possible value of the expected value of this sum.

Constraints

1 ≤ K ≤ N ≤ 200000

1 ≤ p_i ≤ 1000

All values in input are integers.

Input

Input is given from Standard Input in the following format:

N K
p_1 ... p_N

Output

Print the maximum possible value of the expected value of the sum of the numbers shown.

Your output will be considered correct when its absolute or relative error from our answer is at most 10^{-6}.

Sample Input 1

5 3
1 2 2 4 5

Sample Output 1

7.000000000000

When we throw the third, fourth, and fifth dice from the left, the expected value of the sum of the numbers shown is 7. This is the maximum value we can achieve.

Sample Input 2

4 1
6 6 6 6

Sample Output 2

3.500000000000

Regardless of which die we choose, the expected value of the number shown is 3.5.

Sample Input 3

10 4
17 13 13 12 15 20 10 13 17 11

Sample Output 3

32.000000000000

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Accepted)

import java.util.*;
import java.io.*;

public class Main {

    public static void main(String[] args) {
        FastScanner sc = new FastScanner();
        int n = sc.nextInt();
        int k = sc.nextInt();
        int[] p = new int[n];
        for (int i = 0; i < p.length; i++) {
            p[i] = sc.nextInt();
        }

        double[] data  = new double[1010];
        data[0] = 0;
        double sum = 0;
        for (int i = 1; i < data.length; i++) {
            sum += i;
            data[i] = sum / i;
        }

        double max = 0;
        double sum2 = 0;
        for (int i = 0; i < k; i++) {
            sum2 += data[p[i]];
        }
        max = sum2;
        for (int i = k; i < n; i++) {
            sum2 += data[p[i]];
            sum2 -= data[p[i - k]];
            max = Math.max(max, sum2);
        }

        System.out.println(max);
    }

    private static class FastScanner {
        private final InputStream in = System.in;
        private final byte[] buffer = new byte[1024];
        private int ptr = 0;
        private int buflen = 0;
        private boolean hasNextByte() {
            if (ptr < buflen) {
                return true;
            }else{
                ptr = 0;
                try {
                    buflen = in.read(buffer);
                } catch (IOException e) {
                    e.printStackTrace();
                }
                if (buflen <= 0) {
                    return false;
                }
            }
            return true;
        }
        private int readByte() { if (hasNextByte()) return buffer[ptr++]; else return -1;}
        private static boolean isPrintableChar(int c) { return 33 <= c && c <= 126;}
        public boolean hasNext() { while(hasNextByte() && !isPrintableChar(buffer[ptr])) ptr++; return hasNextByte();}
        public String next() {
            if (!hasNext()) throw new NoSuchElementException();
            StringBuilder sb = new StringBuilder();
            int b = readByte();
            while(isPrintableChar(b)) {
                sb.appendCodePoint(b);
                b = readByte();
            }
            return sb.toString();
        }
        public long nextLong() {
            if (!hasNext()) throw new NoSuchElementException();
            long n = 0;
            boolean minus = false;
            int b = readByte();
            if (b == '-') {
                minus = true;
                b = readByte();
            }
            if (b < '0' || '9' < b) {
                throw new NumberFormatException();
            }
            while(true){
                if ('0' <= b && b <= '9') {
                    n *= 10;
                    n += b - '0';
                }else if(b == -1 || !isPrintableChar(b)){
                    return minus ? -n : n;
                }else{
                    throw new NumberFormatException();
                }
                b = readByte();
            }
        }
        public int nextInt() {
            long nl = nextLong();
            if (nl < Integer.MIN_VALUE || nl > Integer.MAX_VALUE) throw new NumberFormatException();
            return (int) nl;
        }
        public double nextDouble() { return Double.parseDouble(next());}
    }
}

class Card{
    int pos;
    boolean red;
    int ir;
    int ib;
    boolean re;

    Card(int pos, int ir, int ib){
        this(pos, true, ir, ib);
    }

    Card(int pos, boolean red, int ir, int ib){
        this.pos = pos;
        this.red = red;
        this.ir = ir;
        this.ib = ib;
        if(pos % 2 == 0){
            re = red;
        }else{
            re = !red;
        }
    }

    int getU(){
        if(red) return ir;
        else return ib;
    }

    int getD(){
        if(red) return ib;
        else return ir;
    }

    boolean exist(int cpos, boolean cred){
        if(cpos % 2 == 0){
            if(cred){
                return re;
            }else{
                return !re;
            }
        }else{
            if(cred){
                return !re;
            }else{
                return re;
            }
        }
    }

    Card copy(){
        return new Card(pos, red, ir, ib);
    }
}