The control of geodesic rays

Let $M$ be a simply-connected, complete Riemannian manifold whose sectional curvature $K_M$ satisfies $-b^2\leq K_M\leq -a^2<0$. Fix two points $p,q$ in $M$, for any geodesic ray $\gamma(t)$ starting from $p$, can we find a geodesic ray $\gamma_1(t)$ starting from $q$ and a constant $C>0$ such that $d(\gamma(t),\gamma_1(t)) \leq C$ for all $t \geq 0$. ($d$ is the distance function on $M$)?