eolymp
bolt
Try our new interface for solving problems
Problems

K-variance

K-variance

Time limit 1 second
Memory limit 128 MiB

Consider the variance of the sequence a[1], a[2], ..., a[n] as

prb11317.gif

where

prb11317_1.gif

Consider the K-variance as the variance of the consecutive subsequence of length k.

Your task is to calculate all (n - k + 1) K-variances for the given sequence and k.

Formally, the i-th (1in - k + 1) K-variance r[i] is the variance of sequence {a[i], a[i+1], ..., a[i+k-1]}.

Input data

The first line contains 2 integers n, m (2mn10^5).The second line of the input contains n integers a[1], a[2], ..., a[n] (|a[i]| ≤ 100).

Output data

Print (n - k + 1) lines with floating numbers r[1], r[2], ..., r[n-k+1].

Your answer will be considered correct if its absolute or relative error does not exceed 10^(-4).

Examples

Input example #1
3 2
1 3 2
Output example #1
1.41421356
0.70710678
Input example #2
5 3
1 3 2 4 5
Output example #2
1.00000000
1.00000000
1.52752523
Source 2022 Azerbaijan ICPC Qualification