A woman in Manhattan is watching the second presidential debate and hears Donald J. Trump say that, no, he has never kissed or groped a woman without her permission. She goes to bed deeply upset. The next morning she writes an email to The New York Times to say, yes, in fact, he has. It happened to her, she says. Mr. Trump denies her account. Michael Barbaro and Megan Twohey tell the story of the days that followed.

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