AquaMoon and Wrong Coordinate

题意翻译

有 $n$ 个人站在一根数轴的正半轴的整点上，他们准备向数轴正方向运动。每个人的运动速度都是整数。 现在记录了他们 $0\sim k-1$ 时刻的坐标集合（即顺序有可能被打乱）共 $nk$ 个数，其中有一个数被修改成了任意值，你需要找出这个数位于哪一个时刻的坐标集合，和它原来应当是什么。第 $0$ 时刻不会被修改。

题目描述

Cirno gives AquaMoon a problem. There are $ m $ people numbered from $ 0 $ to $ m - 1 $ . They are standing on a coordinate axis in points with positive integer coordinates. They are facing right (i.e. in the direction of the coordinate increase). At this moment everyone will start running with the constant speed in the direction of coordinate increasing. The initial coordinate of the $ i $ -th person on the line is $ x_i $ , and the speed of the $ i $ -th person is $ v_i $ . So the coordinate of the $ i $ -th person at the moment $ t $ will be $ x_i + t \cdot v_i $ . Cirno captured the coordinates of $ m $ people in $ k $ consecutive integer moments from $ 0 $ to $ k - 1 $ . In every moment, the coordinates of $ m $ people were recorded in arbitrary order. To make the problem more funny, Cirno modified one coordinate at the moment $ y $ ( $ 0 < y < k-1 $ ) to a different integer. AquaMoon wants to find the moment $ y $ and the original coordinate $ p $ before the modification. Actually, she is not a programmer at all. So she wasn't able to solve it. Can you help her?

输入输出格式

输入格式

This problem is made as interactive. It means, that your solution will read the input, given by the interactor. But the interactor will give you the full input at the beginning and after that, you should print the answer. So you should solve the problem, like as you solve the usual, non-interactive problem because you won't have any interaction process. The only thing you should not forget is to flush the output buffer, after printing the answer. Otherwise, you can get an "Idleness limit exceeded" verdict. Refer to the [interactive problems guide](https://codeforces.com/blog/entry/45307) for the detailed information about flushing the output buffer. The first line contains two integers $ m $ and $ k $ ( $ 5 \leq m \leq 1000 $ , $ 7 \leq k \leq 1000 $ ) — the number of people and the number of recorded moments. The next $ k $ lines contain captured positions. $ i $ -th of these lines contains $ m $ integers between $ 1 $ and $ 10^6 $ (inclusive), representing positions captured by Cirno at the moment $ i-1 $ . The input is guaranteed to be valid (i.e. only one integer was modified to a different value according to the problem statement). Also, it is guaranteed, that $ 1 \le v_i \le 1000 $ for all $ 1 \leq i \leq m $ . Hack format: The first line should contain two integers $ m $ and $ k $ ( $ 5 \leq m \leq 1000 $ , $ 7 \leq k \leq 1000 $ ) — the number of people and the number of moments. In the second line, there should be $ m $ integers $ x_0, x_1, \dots,x_{m - 1} $ ( $ 1 \le x_i \le 10^6 $ ), where $ x_i $ is the initial coordinate of the $ i $ -th person. In the third line, there should be $ m $ integers $ v_0, v_1, \dots,v_{m - 1} $ ( $ 1 \le v_i \le 1000 $ ), where $ v_i $ is the speed of the $ i $ -th person. It should be true that $ x_i + (k-1) v_i \leq 10^6 $ for each $ 0 \leq i < m $ . In the next $ k $ lines, each line should contain $ m $ integers. $ i $ -th line should contain $ m $ distinct integers $ p_0, p_1, \ldots, p_{m-1} $ ( $ 0 \leq p_j < m $ ). The meaning of these numbers: $ j $ -th integer in the input in the $ i $ -th moment is the coordinate of the $ p_{j} $ -th person. In the last line, there should be three integers $ y $ , $ i $ , $ c $ . Cirno modified the coordinate of the $ i $ -th person at the moment $ y $ to $ c $ ( $ 1 \leq y \leq k-2 $ , $ 0 \leq i \leq m - 1 $ , $ 1 \leq c \leq 10^6 $ , $ c \neq x_i + y \cdot v_i $ ).

输出格式

Print a single line with two integers $ y $ , $ p $ — the moment that contains the modified coordinate and the original coordinate.

输入输出样例

输入样例 #1

5 7
6 9 9 6 9
10 7 10 8 10
11 11 11 10 8
12 12 12 12 9
14 13 12 10 13
11 14 16 14 14
12 15 18 15 15

输出样例 #1

4 13

说明

In the first test the initial coordinates of people are $ 9 $ , $ 6 $ , $ 6 $ , $ 9 $ , $ 9 $ and their speeds are $ 1 $ , $ 2 $ , $ 1 $ , $ 1 $ , $ 1 $ . So, it's easy to see, that at the moment $ 4 $ one coordinate was modified from $ 13 $ to $ 12 $ . This is the first test in the hack format: ``` <pre class="verbatim"><br></br>5 7<br></br>9 6 6 9 9<br></br>1 2 1 1 1<br></br>2 3 4 1 0<br></br>0 2 3 1 4<br></br>4 3 0 1 2<br></br>1 3 4 0 2<br></br>1 4 0 2 3<br></br>2 4 1 3 0<br></br>2 4 1 3 0<br></br>4 0 12<br></br> ```