Quartermeter Push Obstacles

Brilli the ant is going from point \(A=(0,0)\) to point \(B=(10,10)\) on a grid. It can either move one unit up or one unit to the right in one move, along the grid lines. The perimeter of the area in which it can move is given in the figure by a quarter circle of radius 10 centred at point \(C=(10,0)\). Along the way it encounters small bead obstacles which can be moved by a unit distance along the direction in which it is moving. So if it is moving from \((2,1)\) to \((2,2)\) and if there is an obstacle at \((2,2)\), then the obstacle moves to \((2,3) \) and Brilli moves to \((2,2)\). There are three obstacles in total, at \((2,2)\), \((4,4) \) and \((7,7)\). The obstacles too are not allowed to cross the perimeter but move along the perimeter, just like Brilli. Find the number of possible paths such that Brilli can reach its destination from point A to point B.

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