Magic-Square With Subtractions Additions

Consider the m by m magic square where some of the sub-squares are shaded in. Like a standard magic square the rows, columns, and main diagonals all total the same value, and the squares are filled with the integers from 1 to m^2. But in this square, the integers in the shaded sub-squares are SUBTRACTED, while those in the unshaded squares are added to the total.

The example I have been working on today (not obsessively), but have failed to come up with a solution, is the m=4 square below:

The ascii-art above looks completely messed up in Google, even though it looked completely fine when I previewed it in Google.

If the columns are labeled {a,b,c,d}, and the rows {1,2,3,4}, then the shaded squares are {a1,c2,b3,d4}.