Maximum Average Subarray

You are given an integer sequence \(a\) of length \(n\), where \(a_i\) denotes the value of the \(i^{th}\) element. A segment is defined as a contiguous subsequence with length in the interval \([S, T]\). The average value of a segment is defined as the sum of the segment's values divided by its length, that is, using LaTeX notation:

\[ \text{Average} = \frac{\text{Sum of segment values}}{\text{Segment length}} \]

Your task is to find the segment with the maximum average among all segments whose lengths are between \(S\) and \(T\) (inclusive).

inputFormat

The input consists of two lines:

• The first line contains three integers \(n\), \(S\), and \(T\) where \(n\) is the length of the sequence and \(S\) and \(T\) define the inclusive range of segment lengths.
• The second line contains \(n\) space-separated integers representing the sequence \(a\).

outputFormat

Output a single number: the maximum average value among all valid segments. Print the answer rounded to 6 decimal places.

sample

5 2 3
1 12 -3 5 7

6.500000