A circle of radius 1 is randomly placed in a 15-by-36 rectangle \(ABCD\) so that the circle lies completely within the rectangle. Given that the probability that the circle will not touch diagonal \(AC\) is \(m/n,\) where \(m\) and \(n\) are relatively prime positive integers, find \(m + n.\)

(第二十二届AIME1 2004 第10题)