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 9.2.1) (judge verdict: Wrong Answer)

#include <bits/stdc++.h>
using namespace std;
#define fi first
#define se second
#define all(a) a.begin(), a.end()
#define pb push_back
#define mp make_pair
typedef long long ll;
typedef pair<ll,ll> P;
typedef pair<ll,int> pli;
typedef pair<int,int> pii;
#define rep(i,a,b) for(ll i=a ; i<b ; i++)
#define qrep(que, ite) for(auto ite=begin(que) ; ite!=end(que) ; ite++)
const int max_n = 1e5;
const ll mod = 1e9+7;
const ll INF = 1e17;
const int inf = 1e5;
typedef long double ld;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
ll gcd(ll a, ll b) { return a ? gcd(b%a, a) : b; }
int dx[4] = {0,0,1,-1};
int dy[4] = {1,-1,0,0};
struct UnionFind {
    vector<int> par;

    UnionFind(int n) : par(n, -1) { }
    void init(int n) { par.assign(n, -1); }

    int root(int x) {
        if (par[x] < 0) return x;
        else return par[x] = root(par[x]);
    }

    bool issame(int x, int y) {
        return root(x) == root(y);
    }

    bool merge(int x, int y) {
        x = root(x); y = root(y);
        if (x == y) return false;
        if (par[x] > par[y]) swap(x, y); // merge technique
        par[x] += par[y];
        par[y] = x;
        return true;
    }

    int size(int x) {
        return -par[root(x)];
    }
};
struct SegmentTree{
  int N;
  vector<int> node;
  public :
    void intit(vector<int>v){
      int sz = v.size();
      N=1;
      while(N<sz) N*=2;
      node.resize(N);
      for(int i=0 ; i<sz ; i++) node[i+N-1] = v[i];
      for(int i=N-2 ; i>=0 ; i--) node[i] = min(node[i*2+1], node[i*2+2]);
    }
    void update(int x, int val){
      x += N-1;
      node[x+N-1] = val;
      while(x>0){
        x = (x-1)/2;
        node[x] = min(node[x*2+1], node[x*2+2]);
      }
    }
    int getmin(int a, int b, int k, int l, int r){
      if(b<=l || r<=a) return inf;
      else if(a<=l && r<=b) return node[k];
      else{
        int vl = getmin(a, b, 2*k+1, l, (l+r)/2);
        int vr = getmin(a, b, 2*k+2, (l+r)/2, r);
        return min(vl, vr);
      }
    }
};
int main(){
  ll N,K; cin>>N>>K;
  vector<ll> v(N);
  rep(i,0,N){
    cin >> v[i];
    v[i]++;
  }
  vector<ll> v2(N+1, 0);
  rep(i,0,N) v2[i+1] = v2[i] + v[i];
  ll res = 0;
  for(ll i=0 ; i+K<=N ; i++){
    chmax(res, v2[i+K] - v2[i]);
  }
  cout << (double)res/2 << endl;
  return 0;
}