Construction in the City
Recent trends have reached Sun City, where a local businessman plans to construct a modern shopping and entertainment complex. Leading architects have already designed the project, and now the only task remaining is to choose its location. Naturally, the entrepreneur wants the complex to be as close to the city center as possible. However, the city administration strictly opposes demolishing any existing buildings. Thus, the entrepreneur must find an available plot that is nearest to the city center and large enough for the construction. Your task is to write a program that solves this problem.
Sun City is known for its round buildings. These buildings do not overlap, though some may touch. The shopping and entertainment complex will also be circular and must not intersect with existing buildings (touching is permissible). The distance from a building to the city center is defined as the distance from the building's center to the city center.
Input
The first line of the input contains two numbers: an integer N (1 ≤ N ≤ 800) and a real number R (0 < R ≤ 10^6), representing the number of existing buildings and the radius of the shopping and entertainment complex, respectively. This is followed by N lines, each containing three numbers x_i, y_i, and r_i—the coordinates of the center and the radius of the i-th building. The coordinates do not exceed 10^6 in absolute value, and the radii are positive and do not exceed 10^6. The coordinate system is set such that the city center is at (0, 0).
Output
In the output, print two numbers: the coordinates of the center of the shopping and entertainment complex. The chosen point must meet the following criteria:
For each i, the distance from the chosen point to the center of the i-th building must be greater than r_i+R-10^{-3}.
The distance from the chosen point to the origin must differ from the optimal by no more than 10^{-3}.