Rotational Geometry at 120°

A point $A$ lies 100 meters from a fixed point $O$. Point $A$ is rotated 120° clockwise about $O$ until it reaches point $B$. The rotation traces a circular arc from $A$ to $B$. What is the exact area of the region enclosed by the arc $AB$ and the chord $AB$? The answer is in the form $\frac{a\pi-b\sqrt{3}}{3}$, where $a$ and $b$ are positive integers. Input the answer as the sum $a+b$.