To divide a line segment $AB$ in the ration $s : t$ (s and t are positive integers with $s : t $$9\; s$ and t are positive integers with $s > t)$, draw a ray AX so that $ \angle BAX$ is an acute angle and then mark points on the ray $AX$ at equal distances such that the minimum number of these points is:

Question

$(A) \; s+t \\(B)\; t \\(C)\; s \\(D)\; s-t $