Let $a_0=5/2$ and $a_k=a^2_{k-1}-2$ for $k\geq1.$ Compute

$$\prod\limits_{k=0}^{\infty}\left(1-\frac{1}{a_k}\right)$$

in closed form.The answer is in the form \frac{m}{n}, where gcd(m, n) = 1. Please provide the value of m + n.

Let's think step by step and output the final answer within \boxed{}.
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