Description

Original source: USACO 2003 Mar. Green

Given a non-negative integer sequence $A$ of length $n$, find a subsegment with the maximum average value, where the length is at least $L$.

Input Format

The first line contains two integers $n$ and $L$ separated by a space;

The second line contains $n$ non-negative integers separated by spaces, representing $A_i$.

Output Format

Output an integer representing $1000$ times this average value. Do not round, output directly.

Sample 1

10 6
6 4 2 10 3 8 5 9 4 1

6500

Data Range and Hints

$1 \leq n \leq 10^5, 0 \leq A_i \leq 2000$.