Let ABCD be a trapezoid with AD \parallel BC, AD = 2, and BC = 1. Let M be the midpoint of AD, and let P be the intersection of BD with CM. Extend AP to meet segment CD at point Q. If the ratio CQ/QD = \frac{a}{b}, where a and b are positive integers and \gcd(a, b) = 1, find a + b.