Cumsum range and values

I am trying to write a loop where each row of the output matrix represents a cumulative sum of the elements of the input matrix, meanwhile adding restrictions ( I only want to the cumulative sum to operate up to the matrix cell/ element that is not zero, or in other words I want to stop the cumsum operation right before the cell value of that particular row is equal to zero) Example: Input row vector A= [1 1 1 2 3 4 5 1 2 1 5 4 1 0 0 0 0 0 0 0 0 0]; so basically I want to get a new vector that operates the cumsum(A) up to the 13th element, which is equal to1) and the rest of the entries need to remain as zeros. can anyone point me in the right direction or maybe suggest a more efficient way of doing this because my actual matrix is (14680*101) dimension.