MATLAB: Only add to empty elements in an array

arrayarray arithmeticMATLAB

Is there a quick way to add an array to another one of equal size, BUT only add if the particular element in the first array is 0?
For example, I start with Original = zeros(3)
I want to add 3 arrays to it. lets say
a = [1 2 3; 0 0 0; 0 0 0]
b = [0 0 0; 4 5 6; 0 0 0]
c = [0 0 0; 1 1 1; 7 8 9]
If I just add a, b, and c to Original I will get [1 2 3; 5 6 7; 7 8 9] but I want the second row of c to NOT add because that row of Original already has values in it.
So it should give Original = [1 2 3; 4 5 6; 7 8 9]
I am looking to use this with 3D arrays, and preferably without for looping through each element.

Best Answer

>> d = cat(3,a,b,c);
>> sum(d.*(cumsum(d~=0,3)==1),3)
ans =
     1     2     3
     4     5     6
     7     8     9
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