I have the following code to align a system of equations
\begin{aligned}
p &= q r &+ r_0 \\
r &= q_0 r_0 &+ r_1 \\
r_0 &= q_1 r_1 &+ r_2 \\
r_k &= q_{k+1} r_{k+1} &+ r_{k+2} \\
&\mathrel{\vdots} \\
r_{k+1} &= q_{k+2} r_{k+2}
\end{aligned}
I can not understand why these equations do not align w.r.t +.
Please help me explain this phenomenon!
align
environment is given in this answer: Aligning equations