Circle \Gamma is centered at (0,0) in the plane with radius 2022 \sqrt{3}. Circle \Omega is centered on the x-axis, passes through the point A=(6066,0), and intersects \Gamma orthogonally at the point P=(x, y) with y>0. If the length of the minor arc A P on \Omega can be expressed as \frac{m \pi}{n} for relatively prime positive integers m, n, find m+n.
(Two circles are said to intersect orthogonally at a point P if the tangent lines at P form a right angle.)