There are N points situated on a straight line. The i-th point is located at coordinate x[i] and has a mass of m[i]. The locat?on of each point is strongly fixed and cannot be changed by any forces. Coordinates of all points are distinct.
When another point P is added on the line and its position is not fixed, the point falls under the impact of gravitational forces from each of the given N points. Points located to the left of P force it to the left, and points located to the right of P force it to the right. When two points are located a distance of d apart and have masses m1 and m2, the value of gravitational force between them is F = G * m1 * m2 / d^2, where G is some positive constant.
Point P is said to be an equilibrium point if the vector sum of gravitational forces from all points on P equals zero. In other words, the sum of the values of gravitational forces between P and all the points located to the left of P must be the same as the sum of the values of gravitational forces between P and all the points located to the right of P.
It is known that there always exist exactly N-1 equilibrium points. Return a double containing their coordinates sorted in ascending order.