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Let $f : R \to R$ be defined by $f(x) = \begin{cases} k-2x, & \quad \text{if } \text{ x $\leq$ -1}\\ 2x + 3, & \quad \text{if } \text{ x > -1} \end{cases} $. If $f$ has a local minimum at $x=-1$, then a possible value of $k$ is

( A ) $-1$
( B ) $1$
( C ) $-\frac{1}{2}$
( D ) $0$

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