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Default SUMPRODUCT on filtered rows

I have a rectangular range of number, with a row header on top of it.
Then I apply a filter.

Say that I want the sumproduct of the visible cells in columns B & C

A B C
1 1 2
0 2 1
1 3 -1
1 2 3
0 1 2

Then I filter on column A equal to 1

The figure that I need is 1*2+3*(-1)+2*3 = 6
If I use the Sumproduct function I get 10, because the rows starting
with 0 are not filtered out.

Can I get the result I want with sumproduct? (I think not)
Can I use Subtotal instead? without using an auxiliary column neither.

Any suggestions?

Please, I do not want to use D as an intermediary column for the
result of B*C

Thank you in advance
 
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