Are You Fired?

Levian works as an accountant in a large company. Levian knows how much the company has earned in each of the $$$n$$$ consecutive months — in the $$$i$$$-th month the company had income equal to $$$a_i$$$ (positive income means profit, negative income means loss, zero income means no change). Because of the general self-isolation, the first $$$\lceil \tfrac{n}{2} \rceil$$$ months income might have been completely unstable, but then everything stabilized and for the last $$$\lfloor \tfrac{n}{2} \rfloor$$$ months the income was the same.

Levian decided to tell the directors $$$n-k+1$$$ numbers — the total income of the company for each $$$k$$$ consecutive months. In other words, for each $$$i$$$ between $$$1$$$ and $$$n-k+1$$$ he will say the value $$$a_i + a_{i+1} + \ldots + a_{i + k - 1}$$$. For example, if $$$a=[-1, 0, 1, 2, 2]$$$ and $$$k=3$$$ he will say the numbers $$$0, 3, 5$$$.

Unfortunately, if at least one total income reported by Levian is not a profit (income $$$\le 0$$$), the directors will get angry and fire the failed accountant.

Save Levian's career: find any such $$$k$$$, that for each $$$k$$$ months in a row the company had made a profit, or report that it is impossible.