I am self-studying william Feller's Probability Theory and It's applications, and I stuck on the following problem concerned with counting the number of dyck paths satisfying a certain property.
Let $a>c>0$ and $b>0$. The number of paths which touch the line $x=a$ and then lead to $(n,c)$ without having touched the line $x=-b$ equals
$$N_{n,2a-c} - N_{n,2a+2b+c}$$
where $N_{n,k}$ is the number of dyck paths from (0,0) to (n,k). From the reflection principle, we have the total number of paths from the origin to $(n,c)$ that touch the line $x=a$ is $N_{n,2a-c}$, and from the answer it seems we reflect that point $(n,2a-c)$ on the line $x=-b$, but I can't figure out why this is the case.