Description

Farmer John's farm consists of a long row of \(n (1 \le n \le 10^5)\) fields. Each field contains a certain number \(m\) of cows, \(1 \le m \le 2\times 10^3\).

FJ wants to build a fence around a contiguous group of these fields in order to maximize the average number of cows per field within that block. The block must contain at least \(f (1 \le f \le n)\) fields, where \(f\) given as input.

Calculate the fence placement that maximizes the average, given the constraint.

Input

Line \(1\): Two space-separated integers, \(n\) and \(f\).

Lines \(2..n+1\): Each line contains a single integer, the number of cows in a field. Line \(2\) gives the number of cows in field \(1\), line \(3\) gives the number in field \(2\), and so on.

Output

Line \(1\): A single integer that is \(1000\) times the maximal average. Do not perform rounding, just print the integer that is \(\frac{1000 \times m}{n}\).

Simplified

给定序列 \(a\)，满足 \(\forall a_k \in \mathbb{N^+}\)，求一个平均数最大的，长度不小于 \(f\) 的（连续的）子段。

Samples

Sample #1

Input

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

Output

6500

Source

算法竞赛进阶指南 POJ