300109: CF24C. Sequence of points
Memory Limit:256 MB
Time Limit:2 S
Judge Style:Text Compare
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Description
Sequence of points
题意翻译
题目给出一个点 $M_0$ 和 $N$ 个点 $N_0,N_1...N_{n-1}$ 。 已知 $M_1$ 和 $M_0$ 关于 $N_0$ 对称,$M_2$ 和 $M_1$ 关于 $N_1$ 对称,以此类推,即 $M_{j-1}$ 和 $M_j$ 关于 $N_{(j-1) \bmod n}$ 对称。现在问 $M_x$ 是多少。 ## 输入格式 第一行两个整数,表示 $N$ 和 $x$ $(1\leq N\leq 10^5$,$1 \leq x \leq 10^{18}$ 且 $N$ 为奇数$)$。下面的 $N + 1$ 行,输入一个点 $M_0$ 和 $N$ 个点 $N_0,N_1...N_{n-1}$。 ## 输出格式 一行,两个整数,表示 $M_x$ 的 $x$ 坐标和 $y$ 坐标。题目描述
You are given the following points with integer coordinates on the plane: $ M_{0},A_{0},A_{1},...,A_{n-1} $ , where $ n $ is odd number. Now we define the following infinite sequence of points $ M_{i} $ : $ M_{i} $ is symmetric to $ M_{i-1} $ according ![](https://cdn.luogu.com.cn/upload/vjudge_pic/CF24C/66e749d7ac58d430b20796b255ca8fcf1e6de8d5.png) (for every natural number $ i $ ). Here point $ B $ is symmetric to $ A $ according $ M $ , if $ M $ is the center of the line segment $ AB $ . Given index $ j $ find the point $ M_{j} $ .输入输出格式
输入格式
On the first line you will be given an integer $ n $ ( $ 1<=n<=10^{5} $ ), which will be odd, and $ j $ ( $ 1<=j<=10^{18} $ ), where $ j $ is the index of the desired point. The next line contains two space separated integers, the coordinates of $ M_{0} $ . After that $ n $ lines follow, where the $ i $ -th line contain the space separated integer coordinates of the point $ A_{i-1} $ . The absolute values of all input coordinates will not be greater then $ 1000 $ .
输出格式
On a single line output the coordinates of $ M_{j} $ , space separated.
输入输出样例
输入样例 #1
3 4
0 0
1 1
2 3
-5 3
输出样例 #1
14 0
输入样例 #2
3 1
5 5
1000 1000
-1000 1000
3 100
输出样例 #2
1995 1995