Let \(F_n\) be the \(n\)th Fibonacci number, where as usual \(F_1 = F_2 = 1\) and \(F_{n + 1} = F_n + F_{n - 1}.\) Then \(\prod_{k = 2}^{100} \left( \frac{F_k}{F_{k - 1}} - \frac{F_k}{F_{k + 1}} \right) = \frac{F_a}{F_b}\) for some positive integers \(a\) and \(b.\) Enter the ordered pair \((a,b).\)
