Number of paths with 1,2,... crosses over a point $m$ between 0 and $x$ in a random walk of $n$ steps

Question

Suppose we have a random walk starting from origin and ending at $x$ with $n$ steps, where the set of points is integers on the number line and the steps allowed are 'right' and 'left'. We know that the total paths satisfying the above statement is $$W(x,n)=\binom{n}{\frac{n+x}{2}}$$ I want to find the number of paths with 1 cross, 2 crosses, and so on over $m$ which is a point located between $0$ and $x$. I figured out $$W(m−1,t)W(2,2)W(x−(m+1),n−t−2)$$ is the total number of paths with 1 cross but I can't generalize it to more crosses.