CF1373G.Pawns

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.

你被给定一个 $n$ 行 $n$ 列的国际象棋棋盘。行从下到上编号为 $1$ 至 $n$，列从左到右编号为 $1$ 至 $n$。第 $x$ 列与第 $y$ 行相交的格子记作 $(x, y)$。此外，第 $k$ 列是一条特殊列。

初始时，棋盘为空。共有 $m$ 次对棋盘的修改操作。在第 $i$ 次操作中，会在棋盘上添加或移除一个兵（pawn）。当前棋盘被称为“良好”的，当且仅当我们能依据以下规则将所有兵全部移动至特殊列：

• 位于格子 $(x, y)$ 的兵可移动至格子 $(x, y + 1)$、$(x - 1, y + 1)$ 或 $(x + 1, y + 1)$；
• 可以进行任意多次此类移动；
• 兵不可移出棋盘边界；
• 每个格子最多只能容纳一个兵。

当前棋盘未必总是“良好”的。为修复它，你可以向棋盘顶部添加新行（即新增的行编号依次为 $n+1, n+2, n+3, \dots$）。

在每次 $m$ 次修改操作之后，请输出一个整数——为使棋盘变为“良好”所需添加的最少行数。

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.

第一行包含三个整数 $n$、$k$ 和 $m$（$1 \le n, m \le 2 \cdot 10^5$；$1 \le k \le n$），分别表示棋盘的大小、特殊列的编号以及操作次数。

接下来有 $m$ 行。第 $i$ 行包含两个整数 $x$ 和 $y$（$1 \le x, y \le n$），分别表示列号和行号。若单元格 $(x, y)$ 中没有棋子，则在该单元格中添加一枚棋子；否则，从该单元格中移除一枚棋子。

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

每次修改后，输出一个整数——为使棋盘变为“好棋盘”所需添加的最少行数。