CF1003C.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 $n$ consecutive days. We have measured the temperatures during these $n$ days; the temperature during $i$-th day equals $a_i$.

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 $x$ to day $y$, we calculate it as $\frac{\sum \limits_{i = x}^{y} a_i}{y - x + 1}$ (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 $k$ consecutive days. For example, if analyzing the measures $[3, 4, 1, 2]$ and $k = 3$, we are interested in segments $[3, 4, 1]$, $[4, 1, 2]$ and $[3, 4, 1, 2]$ (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?

最近几天的气温异常炎热。来自贝尔兰各地的科学家们正在研究气温与天气的变化，并声称今年夏天异常酷热。然而，任何科学论断若能辅以具体数据，听起来都会更加可信；因此，他们决定计算一个能够反映气温高低的具体数值。

贝尔兰国立大学的数学家们提出了一种特殊的“炎热强度值”，其计算方法如下：

假设我们要分析连续 $n$ 天的气温数据。我们已测得这 $n$ 天每天的气温；第 $i$ 天的气温为 $a_i$。

我们将某段连续天数的平均气温定义为该段时间内所有气温测量值的算术平均值。因此，若要分析从第 $x$ 天到第 $y$ 天的平均气温，则计算公式为 $\frac{\sum \limits_{i = x}^{y} a_i}{y - x + 1}$（注意：此处除法不进行任何舍入）。而炎热强度值即为所有长度不少于 $k$ 天的连续子段的平均气温中的最大值。例如，若分析气温序列 $[3, 4, 1, 2]$ 且 $k = 3$，则我们关注的子段为 $[3, 4, 1]$、$[4, 1, 2]$ 和 $[3, 4, 1, 2]$（需找出这些子段平均气温的最大值）。

贝尔兰国立大学已聘请你编写一个程序，用于计算给定时间段的炎热强度值。你能否胜任这项任务？

The first line contains two integers $n$ and $k$ ($1 \le k \le n \le 5000$) — 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 $n$ integers $a_1$, $a_2$, ..., $a_n$ ($1 \le a_i \le 5000$) — the temperature measures during given $n$ days.

第一行包含两个整数 $n$ 和 $k$（$1 \le k \le n \le 5000$）—— 分别表示给定时间段内的天数，以及在计算热强度值时所考虑的区段的最少天数。

第二行包含 $n$ 个整数 $a_1$, $a_2$, ..., $a_n$（$1 \le a_i \le 5000$）—— 表示给定 $n$ 天内的温度测量值。

Print one real number — the heat intensity value, i. e., the maximum of average temperatures over all segments of not less than $k$ consecutive days.

Your answer will be considered correct if the following condition holds: $|res - res_0| \lt 10^{-6}$, where $res$ is your answer, and $res_0$ is the answer given by the jury's solution.

输出一个实数——即热强度值，也就是所有长度不小于 $k$ 的连续天数区间的平均温度的最大值。

若满足 $|res - res_0| \lt 10^{-6}$，则你的答案视为正确，其中 $res$ 是你的答案，$res_0$ 是出题方标准解法给出的答案。