Pawns

题意翻译

$n \times n$ 的棋盘上，第 $k$ 行是特殊行，$(x,y)$ 表示第 $x$ 行，第 $y$ 列，这个位置的兵可以走到 $(x-1,y+1),(x,y+1),(x+1,y+1)$。 每个兵都要走到第 $k$ 行，不能有两个兵重合，可以在棋盘后添加若干列让每个兵都能走到第 $k$行。 初始状态没有兵在棋盘上，现在有 $m$ 个操作，将 $(x,y)$ 的状态改变，有兵则拿掉，没兵则添加。求每次操作后求需要最少要添加几列。

题目描述

You are given a chessboard consisting of $ n $ rows and $ n $ columns. Rows are numbered from bottom to top from $ 1 $ to $ n $ . Columns are numbered from left to right from $ 1 $ to $ n $ . The cell at the intersection of the $ x $ -th column and the $ y $ -th row is denoted as $ (x, y) $ . Furthermore, the $ k $ -th column is a special column. Initially, the board is empty. There are $ m $ changes to the board. During the $ i $ -th change one pawn is added or removed from the board. The current board is good if we can move all pawns to the special column by the followings rules: - Pawn in the cell $ (x, y) $ can be moved to the cell $ (x, y + 1) $ , $ (x - 1, y + 1) $ or $ (x + 1, y + 1) $ ; - You can make as many such moves as you like; - Pawns can not be moved outside the chessboard; - Each cell can not contain more than one pawn. The current board may not always be good. To fix it, you can add new rows to the board. New rows are added at the top, i. e. they will have numbers $ n+1, n+2, n+3, \dots $ . After each of $ m $ changes, print one integer — the minimum number of rows which you have to add to make the board good.

输入输出格式

输入格式

The first line contains three integers $ n $ , $ k $ and $ m $ ( $ 1 \le n, m \le 2 \cdot 10^5; 1 \le k \le n $ ) — the size of the board, the index of the special column and the number of changes respectively. Then $ m $ lines follow. The $ i $ -th line contains two integers $ x $ and $ y $ ( $ 1 \le x, y \le n $ ) — the index of the column and the index of the row respectively. If there is no pawn in the cell $ (x, y) $ , then you add a pawn to this cell, otherwise — you remove the pawn from this cell.

输出格式

After each change print one integer — the minimum number of rows which you have to add to make the board good.

输入输出样例

输入样例 #1

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

输出样例 #1

0
1
2
2
1