Mark and Professor Koro

题意翻译

- 给定一个长度为 $n$ 的序列 $a_1,\cdots,a_n$，你可以每次把两个相等 $a_i$ 和 $a_j$ 扔掉，加进来一个 $a_i+1$。 - 给定 $q$ 次修改，每次将 $a_k$ 修改为 $l$，求每次操作后可能出现的最大数。（经过操作后的）

题目描述

After watching a certain anime before going to sleep, Mark dreams of standing in an old classroom with a blackboard that has a sequence of $ n $ positive integers $ a_1, a_2,\dots,a_n $ on it. Then, professor Koro comes in. He can perform the following operation: - select an integer $ x $ that appears at least $ 2 $ times on the board, - erase those $ 2 $ appearances, and - write $ x+1 $ on the board. Professor Koro then asks Mark the question, "what is the maximum possible number that could appear on the board after some operations?" Mark quickly solves this question, but he is still slower than professor Koro. Thus, professor Koro decides to give Mark additional challenges. He will update the initial sequence of integers $ q $ times. Each time, he will choose positive integers $ k $ and $ l $ , then change $ a_k $ to $ l $ . After each update, he will ask Mark the same question again. Help Mark answer these questions faster than Professor Koro! Note that the updates are persistent. Changes made to the sequence $ a $ will apply when processing future updates.

输入输出格式

输入格式

The first line of the input contains two integers $ n $ and $ q $ ( $ 2\leq n\leq 2\cdot 10^5 $ , $ 1\leq q\leq 2\cdot 10^5 $ ) — the length of the sequence $ a $ and the number of updates, respectively. The second line contains $ n $ integers $ a_1,a_2,\dots,a_n $ ( $ 1\leq a_i\leq 2\cdot 10^5 $ ) Then, $ q $ lines follow, each consisting of two integers $ k $ and $ l $ ( $ 1\leq k\leq n $ , $ 1\leq l\leq 2\cdot 10^5 $ ), telling to update $ a_k $ to $ l $ .

输出格式

Print $ q $ lines. The $ i $ -th line should consist of a single integer — the answer after the $ i $ -th update.

输入输出样例

输入样例 #1

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

输出样例 #1

6
5
4
5

输入样例 #2

2 1
200000 1
2 200000

输出样例 #2

200001

说明

In the first example test, the program must proceed through $ 4 $ updates. The sequence after the first update is $ [2,3,2,4,5] $ . One sequence of operations that achieves the number $ 6 $ the following. - Initially, the blackboard has numbers $ [2,3,2,4,5] $ . - Erase two copies of $ 2 $ and write $ 3 $ , yielding $ [3,4,5,\color{red}{3}] $ . - Erase two copies of $ 3 $ and write $ 4 $ , yielding $ [4,5,\color{red}{4}] $ . - Erase two copies of $ 4 $ and write $ 5 $ , yielding $ [5,\color{red}{5}] $ . - Erase two copies of $ 5 $ and write $ 6 $ , yielding $ [\color{red}{6}] $ . Then, in the second update, the array is changed to $ [2,3,2,4,3] $ . This time, Mark cannot achieve $ 6 $ . However, one sequence that Mark can use to achieve $ 5 $ is shown below. - Initially, the blackboard has $ [2,3,2,4,3] $ . - Erase two copies of $ 2 $ and write $ 3 $ , yielding $ [3,4,3,\color{red}{3}] $ . - Erase two copies of $ 3 $ and write $ 4 $ , yielding $ [3,4,\color{red}{4}] $ . - Erase two copies of $ 4 $ and write $ 5 $ , yielding $ [3,\color{red}{5}] $ . In the third update, the array is changed to $ [2,3,2,1,3] $ . One way to achieve $ 4 $ is shown below. - Initially, the blackboard has $ [2,3,2,1,3] $ . - Erase two copies of $ 3 $ and write $ 4 $ , yielding $ [2,2,1,\color{red}{4}] $ .

**题目大意：**
- 给定一个长度为 $ n $ 的序列 $ a_1, a_2, \cdots, a_n $，你可以每次选择两个相同的数 $ a_i $ 和 $ a_j $，将它们移除，并在序列中加入一个 $ a_i + 1 $。
- 给定 $ q $ 次修改，每次将 $ a_k $ 修改为 $ l $，求每次操作后可能出现的最大数。

**输入输出数据格式：**
- 输入格式：
- 第一行包含两个整数 $ n $ 和 $ q $（$ 2 \leq n \leq 2 \cdot 10^5 $，$ 1 \leq q \leq 2 \cdot 10^5 $）——序列 $ a $ 的长度和更新的次数。
- 第二行包含 $ n $ 个整数 $ a_1, a_2, \cdots, a_n $（$ 1 \leq a_i \leq 2 \cdot 10^5 $）。
- 接下来的 $ q $ 行，每行包含两个整数 $ k $ 和 $ l $（$ 1 \leq k \leq n $，$ 1 \leq l \leq 2 \cdot 10^5 $），表示将 $ a_k $ 更新为 $ l $。
- 输出格式：
- 输出 $ q $ 行，第 $ i $ 行包含一个整数——第 $ i $ 次更新后的答案。**题目大意：** - 给定一个长度为 $ n $ 的序列 $ a_1, a_2, \cdots, a_n $，你可以每次选择两个相同的数 $ a_i $ 和 $ a_j $，将它们移除，并在序列中加入一个 $ a_i + 1 $。 - 给定 $ q $ 次修改，每次将 $ a_k $ 修改为 $ l $，求每次操作后可能出现的最大数。 **输入输出数据格式：** - 输入格式： - 第一行包含两个整数 $ n $ 和 $ q $（$ 2 \leq n \leq 2 \cdot 10^5 $，$ 1 \leq q \leq 2 \cdot 10^5 $）——序列 $ a $ 的长度和更新的次数。 - 第二行包含 $ n $ 个整数 $ a_1, a_2, \cdots, a_n $（$ 1 \leq a_i \leq 2 \cdot 10^5 $）。 - 接下来的 $ q $ 行，每行包含两个整数 $ k $ 和 $ l $（$ 1 \leq k \leq n $，$ 1 \leq l \leq 2 \cdot 10^5 $），表示将 $ a_k $ 更新为 $ l $。 - 输出格式： - 输出 $ q $ 行，第 $ i $ 行包含一个整数——第 $ i $ 次更新后的答案。