(python) How can i sum all the results of a combination in a specific way?

Question

I am trying to find a way to combine 2 lists and then sum the combined list in a specific way. The sum of the 2 previous elements must be summed to the next element.

Ex : the sum of the first combination, ((1, 2), (4,)) , should be (3,7,6), because 1+2=3, 3+4=7, 2+4=6.

And then be printed side by side : ((1, 2), (4,)) (3,7,6) IF it ( both the combination and its sum) do not contain a certain element ( somehow alredy inserted).

Here is my code and my examples:

a=[1,2,3]
b=[4,5,6]

import itertools

sets = [a,b];
ks = [2, 1,] 

combinations = itertools.product(*[itertools.combinations(set, k) for set, k in zip(sets, ks)])

for combination in combinations:
    print (combination)

Answer 1

Straight-forwardly:

for i in itertools.product(*[itertools.combinations(set, k) for set, k in zip(sets, ks)]):
    i_sum = i[0][0] + i[0][1]
    print(i, (i_sum, i_sum + i[1][0], i[0][1] + i[1][0]))

The output:

((1, 2), (4,)) (3, 7, 6)
((1, 2), (5,)) (3, 8, 7)
((1, 2), (6,)) (3, 9, 8)
((1, 3), (4,)) (4, 8, 7)
((1, 3), (5,)) (4, 9, 8)
((1, 3), (6,)) (4, 10, 9)
((2, 3), (4,)) (5, 9, 7)
((2, 3), (5,)) (5, 10, 8)
((2, 3), (6,)) (5, 11, 9)