Computing Sum of Distinct Rows

I'm working in Power Query, and have the following table:

I'd like to add the values of type A and type B together, to produce the following table:

Is this possible in Power Query? I'd prefer not to do this "manually" using cell-specific formulas in Excel. The biggest issue I run into is not being able to reference other rows based on a specific cell value.

Bonus points if you know how to do this, replacing simple summation with a more complicated function.

My guess

I could figure out how to do it if I were able to manipulate the first table into something that looks like

This feels close to a pivot, but not quite.

It is a simple Table.Group operation

M Code from the Advanced Editor

let

//change next line to reflect your actual data source
    Source = Excel.CurrentWorkbook(){[Name="Table4"]}[Content],


    #"Changed Type" = Table.TransformColumnTypes(Source,{{"Year", Int64.Type}, {"Type", type text}, {"Value", Int64.Type}}),
    #"Grouped Rows" = Table.Group(#"Changed Type", {"Year"}, {
        {"Sum", each List.Sum([Value]), type nullable number}})
in
    #"Grouped Rows"

In the User Interface, you would

• navigate to Home=>Transform=>GroupBy
• Then fill out the dialog as shown below
  

By the way, your guess table is, in Power Query, a simple Pivot

Also, in Excel, if you have the latest 365 version, you can reproduce the output using a Table with structured references, so you do not have to deal with varying cell references. For example: =GROUPBY(your_table[[#All],[Year]],your_table[[#All],[Value]],SUM,3,0) will produce the same output as Power Query, and will autoupdate when you change your original data

Output from above Excel formula