First of all, the situation you provided is not a Correctable Error. Second, some important information was left out in order to rule properly. 1.) if no one went into the lane for a rebound, and the official rebounded the ball, I would do what the others wrote and go to the alternating possession. However, 2.) if a player went in because he knew it was a 1 and 1, and rebounded the ball, he should not be penalized for being "on the ball." Consequently, give the ball to the team who had possession when the table sounded the horn.
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