Square \(ABCD\) has side length \(2\). A semicircle with diameter \(\overline{AB}\) is constructed inside the square, and the tangent to the semicircle from \(C\) intersects side \(\overline{AD}\) at \(E\). The length of \(\overline{CE}\) can be expressed in the form \(\frac{k}{m}\), where \(\frac{k}{m}\) is a simplified fraction. Please find the value of \(k + m\).

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