Let \(ABCD\) be a rectangle and let \(\overline{DM}\) be a segment perpendicular to the plane of \(ABCD\). Suppose that \(\overline{DM}\) has integer length, and the lengths of \(\overline{MA}, \overline{MC},\) and \(\overline{MB}\) are consecutive odd positive integers (in this order). Find the volume of pyramid \(MABCD\). The original answer is in the form \(k\sqrt{m}\), please provide the value of \(k + m\).

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