Let \(M\) be the intersection of diagonals of the convex quadrilateral \(ABCD\), where \(m(\widehat{AMB})=60^\circ\). Let the points \(O_1\), \(O_2\), \(O_3\), \(O_4\) be the circumcenters of the triangles \(ABM\), \(BCM\), \(CDM\), \(DAM\), respectively. The original answer is in the form \(\frac{k}{m}\), where k and m are integers. Please give the value of k + m.

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