An addition theorem for finite cyclic groups

The following theorem is proved. Let 2 ⩽ k ⩽ [n4] + 1, and let S be a sequence of 2n − k elements in Zn. Suppose that S does not contain any n-subsequence with 0-sum. Then, one can rearrange S to the type a, …,a, b, …, b, c1, …, c2n-k-u-v, where u ⩾ n − 2k + 3, v ⩾ n − 2k + 3, u + v ⩾ 2n − 2k + 2 and a − b generates Zn.