ILL 1985 Problem 25

Find eight positive integers $n_1, n_2, \dots , n_8$ with the following property:

For every integer $k$ , $-1985 \leq k \leq 1985$ , there are eight integers $a_1, a_2, \dots, a_8$ , each belonging to the set $\{-1, 0, 1\}$ , such that $k=\sum_{i=1}^{8} a_i n_i .$