import math

items = (int(x.strip()) for x in open("input.txt"))
values = {(2020, 3)}
tree = dict()


def tree_up(idx, step=1, offset = 0):
    print(idx, step)
    nxt = tree[(idx, step)] if (idx, step) in tree else None
    appendix = [] if nxt is None else tree_up(nxt+idx, step=step+1, offset=idx)
    return [idx - offset] + appendix


for item in items:
    tmp_values = set(values)
    for elem in values:
        new = (elem[0] - item, elem[1]-1)
        if new == (0, 0):
            vals = tree_up(item)
            print("Found [{}]: Sum={}, Product={}".format(
                ", ".join(map(str, vals)),
                sum(vals),
                math.prod(vals)
            ))
            exit()
        elif new[0] < 0 or new[1] < 0:
            # target value too low or to many sums
            continue
        else:
            tree[new] = item
            tmp_values.add(new)
    values = tmp_values