Maximum Subarray Average with Minimum Length Constraint

Given a sequence of n integers, find a contiguous subarray with length at least m such that its average is maximized. The average of a subarray from index l to r is defined as:

$$\frac{\sum_{i=l}^{r} a_i}{r-l+1}$$

You are to output the maximum average value computed to exactly six decimal places.

inputFormat

The first line contains two integers n and m (1 ≤ m ≤ n). The second line contains n space-separated integers representing the sequence.

outputFormat

Output the maximum average value among all contiguous subarrays with length at least m, formatted to exactly six decimal places.

sample

5 3
1 2 3 4 5

4.000000