Problem:
There is an even number of positive integers $a_1, a_2,...,a_n$. Determine whether there is a division into two sets of equal cardinality $A_1$ and $A_2$ so that the sum of the numbers from $A_1$ is strictly greater than the sum of the numbers from $A_2$, and the difference in the sums (from the larger take the smaller) does not exceed y, where y is the given number, y$\geq$0.
Is the problem polynomially solvable or NP-complete?
Attempts:
I have tried to reduce this problem to the Partition problem but my attempt failed. Is this task polynomially solvable?