Gleb And Pizza

题意翻译

### 题目大意 Gleb 点了披萨，他发现有几片香肠在外皮上，但他讨厌披萨的外皮。 披萨一个半径为 $r$ 的圆，圆心位于原点，披萨中间部分是半径为 $r-d$ 的圆，圆心也在原点。外皮部分就是外面一圈宽为 $d$ 的环。 香肠片也是圆的，对于第 $i$ 片香肠，他的半径为 $r_i$ ，圆心位于 $(x_i,y_i)$ 现在求有多少个香肠片整个都在外皮上。 ### 输入格式 第一行给定两个数 $r$ 和 $d$ 。 第二行一个数 $n$ 表示香肠片数。 接下来有 $n$ 行，每行有 $3$ 个数 $x_i,y_i,r_i$ ，表示第 $i$ 个香肠片的相关信息。 ### 输出格式 一行，表示答案。 translated by Rainy7

题目描述

Gleb ordered pizza home. When the courier delivered the pizza, he was very upset, because several pieces of sausage lay on the crust, and he does not really like the crust. The pizza is a circle of radius $ r $ and center at the origin. Pizza consists of the main part — circle of radius $ r-d $ with center at the origin, and crust around the main part of the width $ d $ . Pieces of sausage are also circles. The radius of the $ i $ -th piece of the sausage is $ r_{i} $ , and the center is given as a pair ( $ x_{i} $ , $ y_{i} $ ). Gleb asks you to help determine the number of pieces of sausage caught on the crust. A piece of sausage got on the crust, if it completely lies on the crust.

输入输出格式

输入格式

First string contains two integer numbers $ r $ and $ d $ ( $ 0<=d&lt;r<=500 $ ) — the radius of pizza and the width of crust. Next line contains one integer number $ n $ — the number of pieces of sausage ( $ 1<=n<=10^{5} $ ). Each of next $ n $ lines contains three integer numbers $ x_{i} $ , $ y_{i} $ and $ r_{i} $ ( $ -500<=x_{i},y_{i}<=500 $ , $ 0<=r_{i}<=500 $ ), where $ x_{i} $ and $ y_{i} $ are coordinates of the center of $ i $ -th peace of sausage, $ r_{i} $ — radius of $ i $ -th peace of sausage.

输出格式

Output the number of pieces of sausage that lay on the crust.

输入输出样例

输入样例 #1

8 4
7
7 8 1
-7 3 2
0 2 1
0 -2 2
-3 -3 1
0 6 2
5 3 1

输出样例 #1

2

输入样例 #2

10 8
4
0 0 9
0 0 10
1 0 1
1 0 2

输出样例 #2

0

说明

Below is a picture explaining the first example. Circles of green color denote pieces of sausage lying on the crust.