$c \geq min(k,q) \quad \textrm{and} \quad k < q$

Here the two paths look like:-

$$P'_{3} = y_{1}, \ldots y_{k},b,y_{k+1} \ldots y_{m}$$

$$P_{2} = x_{1}, \ldots x_{p}, \ldots x_{q}, b, x_{q+1}, \ldots x_{m}$$

What is important is where p is in relation to k. There are two sub cases.