CWMO 2016 Problem 3

Let $n$ and $k$ be integers with $k\leq n-2$ . The absolute value of the sum of elements of any $k$ -element subset of $\{a_1,a_2,\cdots,a_n\}$ is less than or equal to 1. Show that: If $|a_1|\geq1$ , then for any $2\leq i \leq n$ , we have: $$|a_1|+|a_i|\leq2$$