Sum Across a Range Based on a Referential Starting Point

I have a table with the following structure:
a) week numbers (1-12) across the top, on row 1
b) store numbers in Col A
c) a Starting week number in Col B (also weeks 1-12)
d) sales data in F2:Q21

I am trying to find a way to sum sales data for each store based on starting week (values in Col B)

For example
Store 200 (in cell A2) starts in Week 5 (as noted in cell B2), so I would like to sum all of the sales values on that same row starting from week 5 through week 12
Again, the week numbers are also specified in Row 1, the header row of the table

Another example
Store 250 (in cell A3) starts in Week 2 (as noted in Cell B3), so I would like to sum all of the sales values on that same row from weeks 2-12, again with respect to the header row that also contains the week numbers

Each store number will start on a different week, and it's too much of a hassle trying to manually change the sum range each time.
Not sure if there is a way to use a dynamic matching reference (index match sum....) something that matches my start week with the header row, and then sums the range accordingly per store.

Attached is a sample file that demos what I am trying to accomplish, and hopefully sheds better light than my explanation above.

Thanks in advance for any help!

Awesome solutions guys.
These both work perfectly!

Thanks so much for your help.

Originally Posted by newdoverman

This formula takes the Start Week as the OFFSET from column E and sums the 12 values to the right starting with the offset value. Enter this formula in D2 and fill down.

Formula:

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Woah.
Very slick solution.

Thanks!