... the original problem statement may be converted into the following subset sum problem: find the number of ways to gather a subset of nums such that its sum is equal to (target + sum(nums)) / 2.

We can also add another trivial check to our algorithm: if target + sum(nums) is not divisible by 2, we can return 0 because there is no solution (this follows from the last line in our derivation above).

Therefore, the crux of this reformulated problem statement is (in pseudo-code):

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for the set of values up to some value V in nums:\

    for some target sum S:\

        number of ways to attain S =

            number of ways to attain S without V\

            + number of ways to attain S-V with V