Partition partition with constraint of equal size

Question

I see the problem here which is the well know partition problem but with constraint that the size of both sets must be equal.

I look at the answer and I don't understand that why Colin said add max(S)⋅length(S), and run the algorithm as normal would make the size of both sets equal. I think for long time.

And i think that his claim for send s∈S to 1+s⋅length(S) is wrong?

Example:

Initial set: 1 2 3 9

1+s⋅length(S)= 1+s(4)=5 9 13 37

After running the traditional Boolean algorithm, what I got is one set of 5 9 13, another set of 37?

Can anyone explain to me? Especially the max(S)⋅length(S) one.