Fill a list randomly with 2 digits of all possible combinations of them so that the sum of the elements of the list gives a given number

Question

I know that the title I mentioned evokes many other topics already mentioned here (like library itertools) but none could give me a solution. My problem is not complicated to understand. I have 2 digits (say 1 and 2) and I want to put them in a list so that the sum of the numbers in the list gives me a number (say 5) and I need to know all possible combinations from this list there. For example :

a = 1
b = 2
L = [1, 2, 2] -> 5
L = [1, 1, 1, 1, 1] -> 5
L = [1, 1, 1, 2] -> 5
.
.
.

I hope to have been able to describe my problem, it's been more than 2 days that I ream disappointed.

Good day to all

Answer 1

With a slight modification of the idea I showed in the proposed duplicate:

from collections import Counter

def subset_sum(vals, target):
    counts = [[Counter()]] + [[] for _ in range(target)]
    for val in vals:
        for i in range(val, target + 1):
            counts[i] += [c + Counter({val: 1}) for c in counts[i-val]]
    return counts[target]

This gives the result:

>>> for counts in subset_sum(vals=(1, 2), target=5):
...     L = [*counts.elements()]
...     print(L, "->", sum(L))
[1, 1, 1, 1, 1] -> 5
[1, 1, 1, 2] -> 5
[1, 2, 2] -> 5