Sum of Modulo Sums

Given an integer n > 9, for each possible insertion between digits in that integer, insert an addition + and evaluate. Then, take the original number modulo those results. Output the sum total of these operations.

An example with n = 47852:

47852 % (4785+2) = 4769
47852 % (478+52) =  152
47852 % (47+852) =  205
47852 % (4+7852) =  716
-----
5842


Input

A single positive integer in any convenient format, n > 9.

Output

The single integer output following the above construction technique.

Rules

• You don't need to worry about input larger than your language's default type.
• Either a full program or a function are acceptable. If a function, you can return the output rather than printing it.
• Standard loopholes are forbidden.
• This is so all usual golfing rules apply, and the shortest code (in bytes) wins.

Examples

47852 -> 5842
13 -> 1
111 -> 6
12345 -> 2097
54321 -> 8331
3729105472 -> 505598476


K (oK), 31 bytes

Solution:

+/(+/+.:''1_(0,'!#$x)_\:$x)!'x:


Try it online!

Example:

+/(+/+.:''1_(0,'!#$x)_\:$x)!'x:47852
5842


Explanation:

Most of the code goes to building up the lists out of the input. Am wondering if there is a trick I'm missing.

{.:''1_(0,'!#$x)_\:$x}47852
(4 7852
47 852
478 52
4785 2)


Full breakdown:

+/(+/+.:''1_(0,'!#$x)_\:$x)!'x: / the solution
x: / store input as variable x
!'   / mod (!) each-both (')
(                       )     / do this together
$x / string x _\: / cut (_) each-left (\:) ( ) / do this together$x            / string x
#              / count length of the string
!               / til, range 0..n-1
0,'                / prepend 0 to each
1_                    / drop the first one
.:''                      / value (.:) each-each (nested)
+                          / flip rows and columns
+/                           / sum up the columns
+/                              / sum up results of the modulo