Reflecting Simple Walk on 0 to m

Consider the chain on $\{0,1,\dots,m\}$. From an interior state it moves left or right with probability $1/2$ each. From $0$ it stays put with probability $1/2$ and moves to $1$ with probability $1/2$; from $m$ it stays put with probability $1/2$ and moves to $m-1$ with probability $1/2$. Find the stationary distribution.