Let P be a 10-degree monic polynomial with roots r_{1}, r_{2}, \ldots, r_{10} \neq 0 and let Q be a 45-degree monic polynomial with roots \frac{1}{r_{i}}+\frac{1}{r_{j}}-\frac{1}{r_{i} r_{j}} where i<j and i, j \in\{1, \ldots, 10\}. If P(0)=Q(1)=2, then \log _{2}(|P(1)|) can be written as \frac{a}{b} for relatively prime integers a, b. Find a+b.