Cumulative sum of groups

I need the cumlative sum of the second column of Data grouped by (or reset at each change in) the first column of Data please:

Data = [[1;1;1; 2;2;2; 3;3;3], [1;0;1; 0;1;1; 0;1;0]]

Answer = [Data, [1;1;2; 0;1;2; 0;1;1]]

Data =
     1     1
     1     0
     1     1
     2     0
     2     1
     2     1
     3     0
     3     1
     3     0
Answer =
     1     1     1
     1     0     1
     1     1     2
     2     0     0
     2     1     1
     2     1     2
     3     0     0
     3     1     1
     3     0     1

[Stephen23]

@PGrant: please explain the logic of how to calculate Answer: assume that we a stupid and that every step need to be shown to us.

[PGrant]

Like a normal cumsum on column 2 of the Data with the difference being that it needs to restart for every change in column 1 of data resulting in column 3 of Answer. Columns 1 & 2 of Answer are just Data...

Answer 1

[Stephen23]

>> data = [1,1;1,0;1,1;2,0;2,1;2,1;3,0;3,1;3,0];
>> C = accumarray(data(:,1),data(:,2),[],@(v){cumsum(v)});
>> [data,vertcat(C{:})]
ans =
   1   1   1
   1   0   1
   1   1   2
   2   0   0
   2   1   1
   2   1   2
   3   0   0
   3   1   1
   3   0   1

[PGrant]

Thanks so much Stephen. Greatly appreciated!