Let circle C be the image of
x2+y2−2x+4y−4=0
in the line
2x−3y+5=0
and A be the point on C such that OA is parallel to the x-axis and A lies on the right-hand side of the centre O of C.
If B(α,β), with β<4, lies on C such that the length of the arc AB is 61 of the perimeter of C, then β−3α is equal to: