Codeforces Round #494 (Div. 3) C. Intense Heat

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 $\mathrm{nn consecutive\; days.\; We\; have\; measured\; the\; temperatures\; during\; these nn days;\; the\; temperature\; during ii-th\; day\; equals aiai.}$

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 $\mathrm{xx to\; day yy,\; we\; calculate\; it\; as y\sum i=xaiy-x+1\sum i=xyaiy-x+1 (note\; that\; division\; is\; performed\; without\; any\; rounding).\; The heat\; intensity\; value is\; the\; maximum\; of average\; temperatures over\; all\; segments\; of\; not\; less\; than kkconsecutive\; days.\; For\; example,\; if\; analyzing\; the\; measures [3,4,1,2][3,4,1,2] and k=3k=3,\; we\; are\; interested\; in\; segments [3,4,1][3,4,1], [4,1,2][4,1,2] and [3,4,1,2][3,4,1,2] (we\; want\; to\; find\; the\; maximum\; value\; of average\; temperature over\; these\; segments).}$

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 $\mathrm{nn and kk (1\le k\le n\le 50001\le k\le n\le 5000)\; —\; the\; number\; of\; days\; in\; the\; given\; period,\; and\; the\; minimum\; number\; of\; days\; in\; a\; segment\; we\; consider\; when\; calculating heat\; intensity\; value,\; respectively.}$

The second line contains $\mathrm{nn integers a1a1, a2a2,\; ..., anan (1\le ai\le 50001\le ai\le 5000)\; —\; the\; temperature\; measures\; during\; given nn days.}$

Output

Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than $\mathrm{kkconsecutive\; days.}$

Your answer will be considered correct if the following condition holds: $|res-res0|<10-6|res-res0|<10-6,\; where resres is\; your\; answer,\; and res0res0 is\; the\; answer\; given\; by\; the\; jury\text{'}s\; solution.$

Example

input

Copy

4 3
3 4 1 2

output

Copy

2.666666666666667

#include<cstdio>
#include<cstring>
#include<algorithm>
#include<iostream>
#include<string>
#include<vector>
#include<stack>
#include<bitset>
#include<cstdlib>
#include<cmath>
#include<set>
#include<list>
#include<deque>
#include<map>
#include<queue>
#define INF 0x3f3f3f3f;
#define ll long long
ll gcd(ll p,ll q)
{
    return q==0?p:gcd(q,p%q);
}
using namespace std;
const int manx=1e5+10;
double n,k,a[5010],sum[5000],ans;
int main()
{
    cin>>n>>k;
    for(int i=1; i<=n; i++)
        cin>>a[i];
    sum[0]=0;
    for(int i=1; i<=n; i++)
        sum[i]=sum[i-1]+a[i];
    for(int i=k; i<=n; i++)///枚举长度
        for(int j=i; j<=n; j++)
            ans=max(ans,(sum[j]-sum[j-i])/i);
    printf("%.15lf\n",ans);
    return 0;
}