Birthday

题目描述

Anna's got a birthday today. She invited many guests and cooked a huge (nearly infinite) birthday cake decorated by $ n $ banana circles of different sizes. Maria's birthday is about to start in 7 minutes too, and while Anna is older, she decided to play the boss a little. She told Maria to cut the cake by $ k $ straight-line cuts (the cutting lines can intersect) to divide banana circles into banana pieces. Anna has many guests and she wants everyone to get at least one banana piece. That's why she told Maria to make the total number of banana pieces maximum. It's not a problem if some banana pieces end up on the same cake piece — the key is to make the maximum number of banana pieces. Determine what result Maria will achieve.

输入输出格式

输入格式

The first line contains two integers $ n $ and $ k $ — the number of banana circles and the number of cuts Maria should perform ( $ 1<=n<=1000 $ , $ 1<=k<=10^{5} $ ). Next $ n $ lines contain the positions and sizes of the banana circles (all banana circles are round). On the cake the Cartesian coordinate system is defined. Each line contains three integers $ x $ , $ y $ and $ r $ — the coordinates of the center of the corresponding banana piece and its radius ( $ -1000<=x,y<=1000 $ , $ 1<=r<=1000 $ ). It is guaranteed that the banana circles do not intersect, do not touch each other and do not overlap with each other. Pretest 10 is big test with $ n=k=1000 $ .

输出格式

Print the only integer — the largest number of banana pieces that Maria can get after she performs the $ k $ straight-line cuts. Please do not use the %lld specificator to read or write 64-bit integers in C++. It is preferred to use the cin, cout streams or the %I64d specificator.

输入输出样例

输入样例 #1

1 1
0 0 1

输出样例 #1

2

输入样例 #2

3 1
0 0 1
3 0 1
6 0 1

输出样例 #2

6

输入样例 #3

1 3
0 0 1

输出样例 #3

7

题意翻译

在笛卡尔坐标系中给出 $n$ 个圆的圆心坐标 $x,y$ 和半径 $r$。你可以画 $k$ 条直线，求这 $k$ 条直线最多可以把这 $n$ 个圆分成几个部分，输出这个最大值，直线可以相交。