# How can you modify a SUBSET-SUM instance so evaluating a set outputs either 0 or 1?

An SUBSET-SUM instance is a list of $$n$$ integers $$\{ a_1, a_2,… a_n\}$$ and a target $$W$$. To evaluate a set is to find the sum of a selection of numbers in the set. However, I want to know, is it possible to modify the instance, or SUBSET-SUM in general, where evaluating a set outputs $$0$$ if the sum equals $$W$$, and $$1$$ otherwise?

Bonus: Give a list of other NP-complete problems (other than 3SAT, where you evaluate a formula that either outputs $$0$$ or $$1$$ depending on the set of binary variables being passed into it), where evaluating an analogous instance outputs $$0$$ if it satisfies some objective related to the problem and $$1$$ otherwise.