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We introduce to the runtime analysis of evolutionary algorithms two powerful techniques: probability-generating functions and variable drift analysis. They are shown to provide a clean framework for proving sharp upper and lower bounds. As an application, we improve the results by Doerr et al. (GECCO~2010) in several respects. First, the upper bound on the expected running time of the most successful quasirandom evolutionary algorithm for the OneMax function is improved from 1.28n ln n to 0.982n ln n, which breaks the barrier of n ln n posed by coupon-collector processes. Compared to the classical 1+1-EA, whose runtime will for the first time be analyzed with respect to terms of lower order, this represents a speedup by more than a factor of e=2.71...