How to sum up to a specific value in Google Sheets

I have a complicated situation in Google Sheets and I don't know if it there is a possible solution for this in sheets. I have a list of records with various values both positive and negative, the sum of the positive numbers will always exceed the sum of the negative numbers by a large amount. These are the values in Column A and B

I need to do the following:

1. sum entire column B (Values) to get the total
2. using only the records which have positive values, get a list of which records to use to get me closest to the to the sum (the value should exceed the sum and the last record would be reduced to get me to the correct amount) as shown in Column D and E on the screenshot
3. The return I need is the list of the record names and the values to to use for each record, column A will always have unique names

I am currently doing this manually by sorting and just selecting the data like I have done in Column D and E, but there are a lot of other steps that need to happen after this and I'd ideally like to automate this part.

Any solutions would be appreciated

Sample Data

I have researched this but can't find an exact solution. I have written basic apps-scripts in the past but I mostly use and prefer using formulas because of privacy but I am not finding something that fits this situation, so probably need a script

Here is a sample of the what the input data would look like so you can work with it

The expected output would look something similar to this:

What is asked can be done with a plain vanilla spreadsheet formula. Use map(), like this:

=let(
  start, B2, end, B21,
  map(start:end, lambda(c., let(
    sumToEnd, sum(c.:end),
    if(sumToEnd < 0, hstack("No", iferror(ø)),
    if(sumToEnd - c. < 0, hstack("Yes", sumToEnd),
    hstack("Yes", if(sumToEnd - c. < 0, sumToEnd, c.))))
  )))
)

The formula will create the whole result table in one go. See map().