56. Person A and Person B start from points $A$ and $B$ respectively at the same time, heading towards each other. They meet for the first time 100 meters away from point $B$. After the meeting, Person A's speed doubles; Person A reaches $B$ and immediately turns back, catching up with Person B when Person B is still 50 meters away from $A$. Therefore, the distance between $A$ and $B$ is $\qquad$ meters.
answer: 250