# Similar problem to Subset Sum?

I've been trying to search for a problem which I think could be similar to Subset Sum. The definition of the problem would be as follows:

Given k $$\in$$ $$\mathbb{Z}$$ and S = {$$s_1$$,...,$$s_n$$} s.t. $$s_i \in \mathbb{Z}$$, how many subsets $$S' \subseteq S$$ exist s.t. $$\sum S' \geq k$$.

I don't know if this problem has been studied previously, but I can't find anything. Could someone help me?

If you changed it into a decision problem of: 'Is there more (or less) than $$l$$ subsets with $$\Sigma_{s\in S'}s \ge k$$ then this would be a decision problem but since $$l$$ is bounded by $$2^n$$ this is still not in NP. It is surely in PSPACE, but I can't put it anywhere lower in the polynomial hierarchy right now.
• Since it's $\geq k$ and not $=k$, it might actually be polytime, no? Jan 12 at 12:51