Mars rover#5163
The spacecraft "North-2006" has successfully reached Mars, and the rover's descent went as planned. Although the rover is designed to navigate rough terrain, unnecessary risks should be avoided. Ideally, the rover should travel from its starting point to its destination without crossing any craters. "North-2006" captured an image of the area from space. Your task is to write a program that, given this image along with the rover's initial and final coordinates, determines whether there is a safe path for the rover from the starting point to the destination.
Let's formalize the problem.
The photograph of the area is a square with its bottom-left corner at coordinates and its top-right corner at . The rover is considered to be a circle of radius . The photograph shows identifiable craters, each shaped as a circle. The center of the -th crater has coordinates (x_k, y_k), and its radius is r_k. Initially, the rover is located at the bottom-left corner of the map, i.e., its center is at (r, r). The rover's goal is to reach the top-right corner of the map, i.e., the point (1000 - r, 1000 - r). For the path to be considered safe, the rover must not leave the map's boundaries (although it may touch the edges), and it must not drive over a crater (although it may touch one). Craters may overlap, and if one crater is entirely inside another crater, the inner crater can be disregarded.
The first line contains two integers and (0 \leq n, r \leq 100). The next lines each contain a description of a crater: the -th crater is given by three real numbers x_k, y_k, r_k in a single line separated by spaces (0 \leq x_k, y_k, r_k \leq 1000). Each real number contains between and digits after the decimal point.
Print **YES** (in uppercase, without quotes) if there is a safe path for the rover; otherwise, print **NO**.
Example 1