HMMT November 2014 E4

In rectangle $A B C D$ with area 1 , point $M$ is selected on $\overline{A B}$ and points $X, Y$ are selected on $\overline{C D}$ such that $A X<A Y$. Suppose that $A M=B M$. Given that the area of triangle $M X Y$ is $\frac{1}{2014}$, compute the area of trapezoid $A X Y B$.