KöMaL 2016 A670

Let $a_1,a_2,\ldots$ be a sequence of nonnegative integers such that $\sum_{i=1}^{2n} a_{id} \le n$ holds for every pair $(n,d)$ of positive integers. Prove that for every positive integer $K$ , there are some positive integers $N$ and $D$ such that $\sum_{i=1}^{2N} a_{iD} = N-K.$