Let $ n \geq 3$ be an odd integer. We denote by $ [-n,n]$ the set of all integers greater or equal than $ -n$ and less or equal than $ n$. Player $ A$ chooses an arbitrary positive integer $ k$, then player $ B$ picks a subset of $ k$ (distinct) elements from $ [-n,n]$. Let this subset be $ S$. If all numbers in $ [-n,n]$ can be written as the sum of exactly $ n$ distinct elements of $ S$, then player $ A$ wins the game. If not, $ B$ wins. Find the least value of $ k$ such that player $ A$ can always win the game.