Mean of absolute value of asymetric random walk

Question

Let $(W_n)_{n\geq 0}$ be an asymmetric random walk, starting in zero, such that \begin{align*} & P ( W_{n+1} = m+1 \mid W_n = m ) + P ( W_{n+1} = m-1 \mid W_n = m ) =1 \\ \text{ and } p = & P ( W_{n+1} = m+1 \mid W_n = m ) < P ( W_{n+1} = m-1 \mid W_n = m ) = q \end{align*} I try to compute $E |W_n|$ in the following way. Write $W_n = -n + 2B_n$ where $B_n \sim \text{Bin} (n, p)$. Then use the law of the unconscious statistician to get \begin{align*} E | W_n | = \sum _{k=0} ^n |-n + 2k |\cdot \binom{n}{k}\cdot p^k \cdot q ^{n-k}. \end{align*} Unfortunately, I'm stuck now. I don't know how to get further. Does someone has some good advise or insight? Thank you in advance.