Henry decides one morning to do a workout, and he walks 43 of the way from his home to his gym. The gym is 2 kilometers away from Henry's home. At that point, he changes his mind and walks 43 of the way from where he is back toward home. When he reaches that point, he changes his mind again and walks 43 of the distance from there back toward the gym. If Henry keeps changing his mind when he has walked 43 of the distance toward either the gym or home from the point where he last changed his mind, he will get very close to walking back and forth between a point A kilometers from home and a point B kilometers from home. What is ∣A−B∣?<spanclass=′latex−bold′>(A)</span>32<spanclass=′latex−bold′>(B)</span>1<spanclass=′latex−bold′>(C)</span>151<spanclass=′latex−bold′>(D)</span>141<spanclass=′latex−bold′>(E)</span>121