\[\large \sum_{r=1}^{117} \dfrac{1}{2 \left \lfloor \sqrt{r} \right \rfloor +1} = \frac ab \]

If the equation above holds true for positive coprime integers \(a \) and \(b\), enter \(a+b +2\) as your answer.

**Notation:** \( \left \lfloor \cdot \right \rfloor \) denotes the floor function.

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