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 C (GCC 5.4.1) (judge verdict: Accepted)

/*  AUTHOR: AKASH JAIN
*   EMAIL:  akash19jain@gmail.com
*   ID:     akash19jain  
*   DATE:   09-02-2020 17:40:23
*/


// #include<algorithm>
// #include <bits/stdc++.h>
// using namespace std;
 
#include<stdio.h>
#include<math.h>
#include<string.h>
#include<stdlib.h>
#include<stdbool.h>
#include<ctype.h>
#define SC1(x)          scanf("%lld",&x)
#define SC2(x,y)        scanf("%lld%lld",&x,&y)
#define SC3(x,y,z)      scanf("%lld%lld%lld",&x,&y,&z)
#define SCS(x)          scanf("\n%s", x)
#define SCA(a,n)        for(long long i=0;i<n;i++)    scanf("%lld",&a[i]);
#define PF1(x)          printf("%lld\n",x)
#define PF2(x,y)        printf("%lld %lld\n",x,y)
#define PF3(x,y,z)      printf("%lld %lld %lld\n",x,y,z)
#define PFA(a,n)        for(long long i=0;i<n;i++)    printf("%lld ",a[i]); printf("\n");
#define PFN             printf("\n")
#define PFS(x)          printf("%s\n",x)
#define REP(i,n)        for(long long i=0;i<(n);++i)
#define FOR(i,a,b)      for(long long i=(a);i<=(b);++i)
#define FORD(i,a,b)     for(long long i=(a);i>=(b);--i)
#define WHILE(n)        while(n--)
#define MEM(a, b)       memset(a, (b), sizeof(a))
#define ITOC(c)         ((char)(((ll)'0')+c))
#define MID(s,e)        (s+(e-s)/2)
#define SZ(a)           strlen(a)          
#define PI              3.1415926535897932384626433832795
#define DEB(x)          printf("The value of \"%s\" is: %d\n",#x,x)
#define CASES           ll t;SC1(t);while(t--)
#define ABS(a)          ((a>0)?a:-(a))
#define SWAP(a,b)       ll z=a;a=b;b=z
#define SWAPC(a,b)      char z=a;a=b;b=z
#define FLSH            fflush(stdout)
typedef long long ll;
typedef unsigned long long ull;
const ll INF = 1<<29;
const ll MOD = 1000000007;
const ll FMOD = 998244353;
const ll MAX = 10000000005;
const ll MIN = -10000000005;
#define FILEIO(name) \  freopen(name".in", "r", stdin); \   freopen(name".out", "w", stdout);
int cmp(const void * a,const void * b);
long long maxv(long long a,long long b);
long long minv(long long a,long long b);
long long gcd(long long u,long long v);
long long digits(long long n);
bool ispoweroftwo(long long n);
bool isvowel(char x);
ll chartoint(char ch);
ll CEIL(ll x,ll y);
ll FLOOR(ll x,ll y);


int main()
{
    ll n,k;
    SC2(n,k);
    ll arr[n];
    SCA(arr,n);
    //qsort(arr,n,sizeof(arr[0]),cmp);
    double ans=0;
    REP(i,k)
    {
        ll x=arr[i]*(arr[i]+1)/2;
        ans+=(1.0*x)/arr[i];
    }
    double max=ans;
    FOR(i,k,n-1)
    {
        ll x=arr[i]*(arr[i]+1)/2;
        ans+=(1.0*x)/arr[i];
        x=arr[i-k]*(arr[i-k]+1)/2;
        ans-=(1.0*x)/arr[i-k];
        if(max<ans)
            max=ans;

    }
    printf("%.10f\n",max);

    return 0;
}
 
 
//qsort(arr,n,sizeof(arr[0]),cmp);
int cmp (const void * a, const void * b)
{
    if( *(ll*)a - *(ll*)b < 0 ) return 1;
    if( *(ll*)a - *(ll*)b > 0 ) return -1;
        return 0;
}
long long maxv(long long a,long long b)
{
    if(a>b) return a;
        return b;
}
long long minv(long long a,long long b)
{
    if(a<b) return a;
        return b;
}
long long gcd(long long u,long long v)
{
    if (v == 0) return u; 
       return gcd(v, u%v);
}
long long digits(long long n)    //to calculate no of digits in a number
{
    return floor(log10(n))+1;
}
bool ispoweroftwo(long long x)
{
    return x && (!(x&(x-1)));
}
bool isvowel(char x)
{
    return(x=='a' || x== 'e' ||x=='i' || x== 'o' || x=='u' );
}
ll chartoint(char ch)
{
    if(ch>='A' && ch<='Z') return(ch-'A');
    else if(ch>='0' && ch<='9') return (ch-'0');
    else if(ch>='a' && ch<='z') return (ch-'a');
    else return 0;
}
ll CEIL(ll x,ll y)
{
    if(x%y==0) return(x/y);
    else return(x/y +1);
}
 
ll FLOOR(ll x,ll y)
{
    if(x%y==0) return(x/y);
    else return(x/y -1);
}