IMO 1984 LL CAN15

Consider all the sums of the form

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IMO 1984 LL CAN15

Origin: CAN

Problem

Consider all the sums of the form 1985  k=1 ekk5 = \pm15 \pm 25 \pm \cdot \cdot \cdot \pm 19855, where ek = \pm1. What is the smallest nonnegative value attained by a sum of this type?