  Let $G$ be an additive finite abelian group of order $n$, and let $S$ be a
sequence of $n+k$ elements in $G$, where $k\geq 1$. Suppose that $S$ contains
$t$ distinct elements. Let $\sum_n(S)$ denote the set that consists of all
elements in $G$ which can be expressed as the sum over a subsequence of length
$n$. In this paper we prove that, either $0\in \sum_n(S)$ or $|\sum_n(S)|\geq
k+t-1.$ This confirms a conjecture by Y.O. Hamidoune in 2000.
