Task

Given an array x of n floats and window size w, compute the rolling mean and rolling population standard deviation (ddof=0) for every full window. Output the rolling means on the first line and rolling stds on the second line.

Input

• Line 1: two ints n w
• Line 2: n space-separated floats

Output

Two lines, each with n - w + 1 space-separated floats (10 significant digits).

Example

Input:

6 3
1 3 5 4 2 6

Output:

3 4 3.666666667 4
1.632993162 0.8164965809 1.247219129 1.632993162

Scaffolding

def rolling_stats(x: list[float], w: int) -> tuple[list[float], list[float]]: ...

Notes

Track A: NumPy only. Use np.lib.stride_tricks.sliding_window_view or a loop. Population std divides by w, not w-1.