Educational Codeforces Round 21 B.Average Sleep Time 前缀和，双指针

题目：

B. Average Sleep Time

time limit per test

1 second

memory limit per test

256 megabytes

input

standard input

output

standard output

It's been almost a week since Polycarp couldn't get rid of insomnia. And as you may already know, one week in Berland lasts k days!

When Polycarp went to a doctor with his problem, the doctor asked him about his sleeping schedule (more specifically, the average amount of hours of sleep per week). Luckily, Polycarp kept records of sleep times for the last n days. So now he has a sequence a1, a2, ..., an, where ai is the sleep time on the i-th day.

The number of records is so large that Polycarp is unable to calculate the average value by himself. Thus he is asking you to help him with the calculations. To get the average Polycarp is going to consider k consecutive days as a week. So there will be n - k + 1 weeks to take into consideration. For example, if k = 2, n = 3 and a = [3, 4, 7], then the result is .

You should write a program which will calculate average sleep times of Polycarp over all weeks.

Input

The first line contains two integer numbers n and k (1 ≤ k ≤ n ≤ 2·105).

The second line contains n integer numbers a1, a2, ..., an (1 ≤ ai ≤ 105).

Output

Output average sleeping time over all weeks.

The answer is considered to be correct if its absolute or relative error does not exceed 10 - 6. In particular, it is enough to output real number with at least 6 digits after the decimal point.

Examples

input

3 23 4 7

output

9.0000000000

input

1 110

output

10.0000000000

input

8 21 2 4 100000 123 456 789 1

output

28964.2857142857

比较简单的一个题，昨晚打virtue contest 却死活没写出来，然后关机睡觉。

其实就是一个模拟嘛。sum[i]：=前i项和。

res+=(sum[i]-sum[j])/weeks(ps,i可以写成j+k无本质区别)

放在这儿，提醒自己基本功不能丢。

code:

#include<cstdio>
typedef long long LL;
const int MAXN=2e5+5;
LL sum[MAXN];
int main(){
    int n,k;scanf("%d%d",&n,&k);
    double divide=(double)1.0*n-k+1;
    for(int i=1;i<=n;++i){
        int a;scanf("%d",&a);
        sum[i]=sum[i-1]+a;
    }
    double res=0.0;
    int i=0,j=k;
    for(;j<=n;){
        res+=(sum[j]-sum[i])/divide;
        ++j;++i;
    }
    printf("%.8f\n",res);
}