2018 IMO Shortlist C1

Let $n \geq 3$ be an integer. Prove that there exists a set $S$ of $2 n$ positive integers satisfying the following property: For every $m=2,3, \ldots, n$ the set $S$ can be partitioned into two subsets with equal sums of elements, with one of subsets of cardinality $m$. (Iceland)

设 $n \geq 3$ 为整数。证明存在一个由 $2 n$ 个正整数组成的集合 $S$，满足以下性质：对于每个 $m=2,3, \ldots, n$，集合 $S$ 可以划分为两个元素总和相等的子集，其中一个子集的基数为 $m$。 (冰岛)