KöMaL 2024 A872

For every positive integer $k$ let $a_{k,1},a_{k,2},\ldots$ be a sequence of positive integers. For every positive integer $k$ let sequence $\{a_{k+1, i}\}$ be the difference sequence of $\{a_{k, i}\}$, i.e. for all positive integers $k$ and $i$ the following holds: $a_{k, i+1}-a_{k, i}=a_{k+1, i}$. Is it possible that every positive integer appears exactly once among numbers $a_{k,i}$?