Hypothesis Tests · Challenge problem

In an A/B test, 45 of 200 users shown design B click a button. Design A is also shown to 200 users. The pooled two-proportion $z$ test, $z = \dfrac{\hat p_A - \hat p_B}{\sqrt{\hat p(1-\hat p)(\tfrac1{200} + \tfrac1{200})}}$ with $\hat p$ the pooled proportion, rejects $H_0\!: p_A = p_B$ when $|z| > 1.96$. What is the smallest number of clicks on design A that leads to rejection with $\hat p_A > \hat p_B$?