NEKO's Maze Game

### 题目描述 NEKO#ΦωΦ 刚刚给自己的电脑添加了一款新的迷宫游戏！ 这个游戏的主要谜题，是一个在 $2 \times n$ 的矩形网格上的迷宫。NEKO 的任务是操控女主角 Nekomimi 从格子 $(1, 1)$ 开始，移动到位于格子 $(2, n)$ 的大门处，并离开迷宫。女主角只能在有公共边的两个格子之间移动。 然而在游戏的某些时刻，有些格子会改变它们的状态：从正常的地面变成岩浆（禁止移动到岩浆格子上）或反过来（让该格子再次变得能够通行）。游戏刚开始时，每个格子都是正常的地面。 当直播过去了数个小时后，NEKO 才终于弄明白了，只有 $q$ 个这样的时刻：第 $i$ 个时刻会翻转格子 $(r_i, c_i)$ 的状态（从地面变成岩浆或相反）。 知道了这些后，NEKO 想问在每个时刻结束后，还是否有可能从格子 $(1, 1)$ 移动到格子 $(2, n)$，并且不经过岩浆格子。 虽然 NEKO 是一个硬核玩家兼热门主播，她还是没有足够的[脑力](https://www.bilibili.com/video/av5299187)去解答这些问题。你可以帮帮她吗？ ### 输入格式 第一行输入两个整数 $n, q$。 接下来 $q$ 行，第 $i$ 行输入两个整数 $r_i, c_i$，表示第 $i$ 个时刻被翻转状态的格子的坐标。 保证格子 $(1, 1)$ 和 $(2, n)$ 不会在给出的坐标中出现。 **数据范围：**$2 \le n \le {10}^5$，$1 \le q \le {10}^5$，$1 \le r_i \le 2$，$1 \le c_i \le n$。 ### 输出格式 输出 $q$ 行，对于每个时刻，如果可能从格子 $(1, 1)$ 移动到格子 $(2, n)$，输出 `Yes`，否则输出 `No`。 你可以以任意大小写输出单词。 ### 样例解释 样例的通关教程在此： - 在第一个时刻后，女主角仍然可以到达终点。这是某一条最短路径：$(1, 1) \to (1, 2) \to (1, 3) \to (1, 4) \to (1, 5) \to (2, 5)$。 - 在第二个时刻后，无法到达终点，这是因为最远能够到达的格子是 $(1, 3)$。 - 在第四个时刻后，格子 $(2, 3)$ 可以通行了，但是整个第四列都无法通行，所以还是无法到达终点。 - 在第五个时刻后，屏障被消除了，于是她又能够到达终点了。

[3R2 as DJ Mashiro - Happiness Breeze](https://open.spotify.com/track/2qGqK8GRS65Wlf20qUBEak) [Ice - DJ Mashiro is dead or alive](https://soundcloud.com/iceloki/dj-mashiro-is-dead-or-alive) NEKO#ΦωΦ has just got a new maze game on her PC! The game's main puzzle is a maze, in the forms of a $ 2 \times n $ rectangle grid. NEKO's task is to lead a Nekomimi girl from cell $ (1, 1) $ to the gate at $ (2, n) $ and escape the maze. The girl can only move between cells sharing a common side. However, at some moments during the game, some cells may change their state: either from normal ground to lava (which forbids movement into that cell), or vice versa (which makes that cell passable again). Initially all cells are of the ground type. After hours of streaming, NEKO finally figured out there are only $ q $ such moments: the $ i $ -th moment toggles the state of cell $ (r_i, c_i) $ (either from ground to lava or vice versa). Knowing this, NEKO wonders, after each of the $ q $ moments, whether it is still possible to move from cell $ (1, 1) $ to cell $ (2, n) $ without going through any lava cells. Although NEKO is a great streamer and gamer, she still can't get through quizzes and problems requiring large amount of Brain Power. Can you help her?

The first line contains integers $ n $ , $ q $ ( $ 2 \le n \le 10^5 $ , $ 1 \le q \le 10^5 $ ). The $ i $ -th of $ q $ following lines contains two integers $ r_i $ , $ c_i $ ( $ 1 \le r_i \le 2 $ , $ 1 \le c_i \le n $ ), denoting the coordinates of the cell to be flipped at the $ i $ -th moment. It is guaranteed that cells $ (1, 1) $ and $ (2, n) $ never appear in the query list.

For each moment, if it is possible to travel from cell $ (1, 1) $ to cell $ (2, n) $ , print "Yes", otherwise print "No". There should be exactly $ q $ answers, one after every update. You can print the words in any case (either lowercase, uppercase or mixed).

5 5
2 3
1 4
2 4
2 3
1 4

Yes
No
No
No
Yes

We'll crack down the example test here: - After the first query, the girl still able to reach the goal. One of the shortest path ways should be: $ (1,1) \to (1,2) \to (1,3) \to (1,4) \to (1,5) \to (2,5) $ . - After the second query, it's impossible to move to the goal, since the farthest cell she could reach is $ (1, 3) $ . - After the fourth query, the $ (2, 3) $ is not blocked, but now all the $ 4 $ -th column is blocked, so she still can't reach the goal. - After the fifth query, the column barrier has been lifted, thus she can go to the final goal again.