Rolling Variance

题号：NC52818
时间限制：C/C++/Rust/Pascal 1秒，其他语言2秒
空间限制：C/C++/Rust/Pascal 32 M，其他语言64 M
Special Judge, 64bit IO Format: %lld

题目描述

Bobo learnt that the *variance* of a sequence $a_1, a_2, \dots, a_n$ is
$\sqrt{\frac{\sum_{i = 1}^n (a_i - \bar{a})^2}{n - 1}}$
where
$\bar{a} = \frac{\sum_{i = 1}^n a_i}{n}.$

Bobo has a sequence $a_1, a_2, \dots, a_n$ ,
and he would like to find the *variance* of each consecutive subsequences of length m.
Formally, the i-th ( $1 \leq i \leq n - m + 1$ ) rolling variance $r_i$ is the *variance* of sequence $\{a_i, a_{i + 1}, \dots, a_{i + m - 1}\}$ .

输入描述:

The input contains at most 30 sets. For each set:
The first line contains 2 integers n, m .
The second line contains n integers  ().

输出描述:

For each set, (n - m + 1) lines with floating numbers .
Your answer will be considered correct if its absolute or relative error does not exceed .

示例1

输入

复制

3 2
1 3 2

输出

复制

1.41421356
0.70710678

示例2

输入

复制

5 3
1 3 2 4 5

输出

复制

1.00000000
1.00000000
1.52752523