Say we have a prime $p$, and its primitive root modulus $g$. Now if we have a number $x \equiv g^{2a}$ mod $p$ for $0 \le a \le p-1$, then its two quadratic residues $r_1 \equiv g^a$ mod $p$ and $r_2 \equiv g^{a+\frac{p-1}{2}}$ mod $p$ can be obtained using the Tonelli-Shanks algorithm.
As far as I understand, the algorithm can return either of the solution pairs $(r_1,r_2)$ or $(r_2,r_1)$. My question is that whether there's a way to know from the obtained roots, which one is precisely $g^a$ and which one is not?