Column-wise summation of overlapping slices Task

Given a list of integers L and another integer s, the goal is to compute the column-wise sums of all s-length (potentially overlapping) slices of L, while pertaining their positions relative to L (see below).

Definitions

The s-length (overlapping) slices of the list L are all the contiguous subsequences (without wrapping) of L that are of length s.

In order to pertain the positions of the slices s relative to L, you can imagine building a "ladder", where each slice si has an offset of i positions from the beginning.



Specs


s is an integer higher than 1 and strictly smaller than the length of L.
L will always contain at least 3 elements.
You can compete in any programming language and can take input and provide output through any standard method, while taking note that these loopholes are forbidden by default. This is code-golf, so the shortest submission (in bytes) for every language wins.


Examples and Test Cases

Here is a worked example:

[1, 2, 3, 4, 5, 6, 7, 8, 9], 3

[1, 2, 3]
   [2, 3, 4]
      [3, 4, 5]
         [4, 5, 6]
            [5, 6, 7]
               [6, 7, 8]
                  [7, 8, 9]
-------------------------------- (+)  | column-wise summation
[1, 4, 9, 12, 15, 18, 21, 16, 9]


And some more test cases:

[1, 3, 12, 100, 23], 4         -&gt; [1, 6, 24, 200, 23]
[3, -6, -9, 19, 2, 0], 2       -&gt; [3, -12, -18, 38, 4, 0]
[5, 6, 7, 8, 2, -4, 7], 3      -&gt; [5, 12, 21, 24, 6, -8, 7]
[1, 2, 3, 4, 5, 6, 7, 8, 9], 3 -&gt; [1, 4, 9, 12, 15, 18, 21, 16, 9]
[1, 1, 1, 1, 1, 1, 1], 6       -&gt; [1, 2, 2, 2, 2, 2, 1]
[1, 2, 3, 4, 5, 6, 7, 8, 9], 6 -&gt; [1, 4, 9, 16, 20, 24, 21, 16, 9]
J, 11, 9 8 bytes

-1 byte thanks to miles!

[:+//.]\


How it works?

The left argument is s, the right one - L

]\ - splits L into sublists with length s

/. - extracts the oblique diagonals (anti-diagonals)

+/ - adds them up

[: - makes a fork from the above verbs

Here's an example J session for the first test case:

   a =. 1 2 3 4 5 6 7 8 9

   ] 3 ]\ a 
1 2 3
2 3 4
3 4 5
4 5 6
5 6 7
6 7 8
7 8 9

   ] &lt;/. 3 ]\ a 
┌─┬───┬─────┬─────┬─────┬─────┬─────┬───┬─┐
│1│2 2│3 3 3│4 4 4│5 5 5│6 6 6│7 7 7│8 8│9│
└─┴───┴─────┴─────┴─────┴─────┴─────┴───┴─┘

   ] +//. 3 ]\ a 
1 4 9 12 15 18 21 16 9


Try it online!