Construction-2#579
On the construction site, there are two trees. According to the work plan, both trees are within the area designated for a future flower bed, which is a circle. It is necessary to enclose these trees with a triangular fence so that the fence lies entirely inside the flower bed.
On the plan, the trees are represented as circles, which may intersect or even be nested within one another (the trees might have grown together due to local environmental pollution, which is unavoidable during construction). They are situated inside the circle representing the flower bed, and may touch its boundary.
Write a program that, based on the information about the flower bed and the trees, determines whether it is possible to construct a triangular fence that does not extend beyond the boundaries of the flower bed (its vertices may lie on the boundary) and contains both trees inside (the fence and trees may touch).
The input consists of information about three circles, each given by the coordinates of its center and its radius. All numbers are integers, with absolute values not exceeding . The radius is a natural number. The first circle represents the flower bed, the second and third circles represent the trees and are inside the first circle.
If it is impossible to enclose the trees with a fence without going beyond the boundaries of the flower bed, output impossible. Otherwise, on the first line output possible, and on the subsequent lines print the coordinates of the vertices of the required triangle. If there are multiple solutions, output any one of them.
Example 1