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.

-----Input-----
The first line of input contains two integers $N$ ($1 \leq N \leq 3 \cdot 10^5$) and $K$ ($1 \leq K \leq N$). The second line of input contains $N$ integers $a_ i$ ($1 \leq a_ i \leq 10^6$).

-----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.

-----Examples-----
Sample Input 1:
4 1
1 2 3 4
Sample Output 1:
4.000000

Sample Input 2:
4 2
2 4 3 4
Sample Output 2:
3.666666

Source: kattis | Difficulty: HARD


Solutions: