PL-OM 2023 Problem 1

Given a sequence of positive integers $a_1, a_2, a_3, \ldots$ such that for any positive integers $k$ , $l$ we have $k+l ~ | ~ a_k + a_l$ . Prove that for all positive integers $k > l$ , $a_k - a_l$ is divisible by $k-l$ .