Description

You are given an array of $N$ integers. Find a consecutive subsequence of numbers of the length at least $K$ that has the maximal possible average.

Please note: the average of a subsequence is the sum of all the numbers in the subsequence divided by its length.

Input

The first line of input contains two integers $N$ ($1 \leq N \leq 3 \times 10^5$) and $K$ ($1 \leq K \leq N$). The second line of input contains $N$ integers ai ($1 \leq a_i \leq 10^6$).

Output

The first and only line of output must contain the maximal possible average. An absolute deviation of $\pm 0.001$ from the official solution is permitted.

4 1
1 2 3 4

4.000000

4 2
2 4 3 4

3.666666

6 3
7 1 2 1 3 6

3.333333

Scoring

In test cases worth $30\%$ of total points, it will hold that $N$ is not larger than $5000$.