302204: CF420E. Playing the ball

Memory Limit:256 MB Time Limit:2 S
Judge Style:Text Compare Creator:
Submit:0 Solved:0

Description

Playing the ball

题目描述

A coder cannot sit and code all day. Sometimes it is a good idea to rise from the desk, have a rest, have small talk with colleagues and even play. The coders of the F company have their favorite ball game. Let's imagine the game on the plane with a cartesian coordinate system. The point (0, 0) contains the player who chooses an arbitrary direction and throws a ball in that direction. The ball hits the plane at distance $ d $ from the player's original position and continues flying in the same direction. After the ball hits the plane for the first time, it flies on and hits the plane again at distance $ 2·d $ from the player's original position and so on (it continue flying in the chosen direction and hitting the plane after each $ d $ units). All coders in the F company are strong, so the ball flies infinitely far away. The plane has $ n $ circles painted on it. If a ball hits the plane and hits a circle that is painted on the plane (including its border), then the player gets one point. The ball can hit multiple circles at once and get one point for each of them (if the ball hits some circle $ x $ times during the move, the player also gets $ x $ points). Count the maximum number of points a player can get if he throws a ball in the arbitrary direction. Note that the direction may have real cooridinates.

输入输出格式

输入格式


The first line contains two space-separated integers — $ n $ и $ d $ $ (1<=n<=2·10^{4}; 5<=d<=10) $ . Next $ n $ lines contain the circles' description. The $ i $ -th line contains three space-separated integers $ x_{i} $ , $ y_{i} $ , $ r_{i} $ $ (-10000<=x_{i},y_{i}<=10000; 1<=r<=50) $ , where $ (x_{i},y_{i},r_{i}) $ are the coordinates of the center and the radius of the circle, correspondingly. The point (0, 0) is not inside or on the border of some circle.

输出格式


Print a single integer — the maximum number of points you can get.

输入输出样例

输入样例 #1

2 5
1 1 1
5 0 1

输出样例 #1

1

输入样例 #2

2 5
4 0 3
5 3 1

输出样例 #2

2

输入样例 #3

1 10
20 0 10

输出样例 #3

3

Input

题意翻译

现有一平面直角坐标系,你在原点 $(0,0)$ 处,向某一方向丢出一小球。小球沿该方向一直飞行,每经过 $d$ 的距离就碰撞一次平面,然后保持方向不变继续飞行。小球可以飞至无穷远处。 坐标系中有 $n$ 个圆。如果小球在碰撞平面时处于某一圆内(包括边界),得一分。球可以一次处在多个圆内,并且对于它们每一个得一分。现在需要确定小球飞行方向使得分最大。输出最大得分。

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