First rotate counterclockwise over 90 degrees:
The new rectangle is $(W,H)=(787,608)$. So the scaling in x-direction is $\,W/h=787/686\,$ and the scaling in y-direction is $\,H/w=608/530\,$, but upon calculation they turn out to be the same, within the required accuracy (= one pixel).
Perform the scaling and round to integer values: $$ \begin{cases} P = q \times W/h = 59 & ; & Q = (w-a-p) \times H/w = 274 \\ A = b \times W/h = 62 & ; & B = a \times H/w = 182 \end{cases} $$