Hokkaido Rail Pass Hamanasu

Does anyone knows wich part of the Hamanasu express trip from aomori to hakodate (or viceversa) is covered by the jr hokkaido pass?
If is not fully covered... how much extra do i have to pay if ialready purchased the hokkaido pass?
It is not clear on the web page (the clear thing there is, you can only take the reserved and unreserved seat but not the carpet car).

It is fully covered only between Sapporo and Hakodate. South of Hakodate, the train does not stop anywhere but in Aomori which is outside the area covered by the Hokkaido Rail Pass. Nevertheless, if you were to ride the Hamanasu between Aomori and Hakodate, the section between Nakaoguni and Hakodate would be covered, and you would just need to pay the fare for the section between Aomori and Nakaoguni.

Nakaoguni Station is the border station between JR Hokkaido and JR East.

According to my calculation, the supplement for a non-reserved seat would be 1070 yen (540 yen for the base fare and 530 yen for the express fee). If you were to travel by reserved seat, I think an additional supplement of 310 (regular season) or 510 yen (peak season) would apply.

Thank you Uji san for your excellent answer