CF1862G.The Great Equalizer

Tema bought an old device with a small screen and a worn-out inscription "The Great Equalizer" on the side.

The seller said that the device needs to be given an array $a$ of integers as input, after which "The Great Equalizer" will work as follows:

1. Sort the current array in non-decreasing order and remove duplicate elements leaving only one occurrence of each element.
2. If the current length of the array is equal to $1$, the device stops working and outputs the single number in the array — output value of the device.
3. Add an arithmetic progression {$n,\ n - 1,\ n - 2,\ \ldots,\ 1$} to the current array, where $n$ is the length of the current array. In other words, $n - i$ is added to the $i$-th element of the array, when indexed from zero.
4. Go to the first step.

To test the operation of the device, Tema came up with a certain array of integers $a$, and then wanted to perform $q$ operations on the array $a$ of the following type:

1. Assign the value $x$ ($1 \le x \le 10^9$) to the element $a_i$ ($1 \le i \le n$).
2. Give the array $a$ as input to the device and find out the result of the device's operation, while the array $a$ remains unchanged during the operation of the device.

Help Tema find out the output values of the device after each operation.

特玛买了一台旧设备，屏幕很小，侧面有一行磨损的铭文：“伟大的均衡器”。

卖家称，该设备需要输入一个整数数组 $a$，之后“伟大的均衡器”将按如下方式工作：

1. 将当前数组按非递减顺序排序，并去除重复元素，使每个元素仅保留一次。
2. 若当前数组长度为 $1$，则设备停止工作，并输出数组中唯一的那个数——即设备的输出值。
3. 向当前数组添加一个等差数列 $\{n,\ n - 1,\ n - 2,\ \ldots,\ 1\}$，其中 $n$ 是当前数组的长度。换言之，对从零开始索引的第 $i$ 个元素，加上 $n - i$。
4. 返回第一步。

为测试设备运行情况，特玛构思了一个整数数组 $a$，并希望对数组 $a$ 执行 $q$ 次如下类型的操作：

1. 将位置 $a_i$（$1 \le i \le n$）的元素赋值为 $x$（$1 \le x \le 10^9$）。
2. 将数组 $a$ 作为输入提供给设备，并求出设备运行后得到的结果；注意：在设备运行过程中，数组 $a$ 本身保持不变。

请帮助特玛求出每次操作后设备的输出值。

The first line of the input contains a single integer $t$ ($1 \le t \le 10^4$) — the number of test cases.

Then follows the description of each test case.

The first line of each test case contains a single integer $n$ ($1 \le n \le 2 \cdot 10^5$) — the size of the array $a$ that Tema initially came up with.

The second line of each test case contains $n$ integers $a_1, a_2, a_3, \ldots, a_n$ ($1 \le a_i \le 10^9$) — the elements of the array $a$.

The third line of a set contains a single integer $q$ ($1 \le q \le 2 \cdot 10^5$) — the number of operations.

Each of the next $q$ lines of a test case contains two integers $i$ ($1 \le i \le n$) and $x$ ($1 \le x \le 10^9$) - the descriptions of the operations.

It is guaranteed that the sum of the values of $n$ and the sum of the values of $q$ for all test cases do not exceed $2 \cdot 10^5$.

输入的第一行包含一个整数 $t$（$1 \le t \le 10^4$）—— 表示测试用例的数量。

随后是每个测试用例的描述。

每个测试用例的第一行包含一个整数 $n$（$1 \le n \le 2 \cdot 10^5$）—— 表示 Tema 最初构造的数组 $a$ 的大小。

每个测试用例的第二行包含 $n$ 个整数 $a_1, a_2, a_3, \ldots, a_n$（$1 \le a_i \le 10^9$）—— 表示数组 $a$ 的元素。

每个测试用例的第三行包含一个整数 $q$（$1 \le q \le 2 \cdot 10^5$）—— 表示操作的数量。

接下来的 $q$ 行，每行包含两个整数 $i$（$1 \le i \le n$）和 $x$（$1 \le x \le 10^9$）—— 表示一次操作的描述。

保证所有测试用例中 $n$ 的总和与 $q$ 的总和均不超过 $2 \cdot 10^5$。

For each test case, output $q$ integers — the output values of the device after each operation.

对于每个测试用例，输出 $q$ 个整数——即设备在每次操作后的输出值。

Let's consider the first example of the input.

Initially, the array of numbers given as input to the device will be $[6, 4, 8]$. It will change as follows: $$[6, 4, 8] \rightarrow [4, 6, 8] \rightarrow [7, 8, 9] \rightarrow [10, 10, 10] \rightarrow [10]$$

Then, the array of numbers given as input to the device will be $[6, 10, 8]$. It will change as follows: $$[6, 10, 8] \rightarrow [6, 8, 10] \rightarrow [9, 10, 11] \rightarrow [12, 12, 12] \rightarrow [12]$$

The last array of numbers given as input to the device will be $[6, 10, 1]$. It will change as follows: $$[6, 10, 1] \rightarrow [1, 6, 10] \rightarrow [4, 8, 11] \rightarrow [7, 10, 12] \rightarrow [10, 12, 13] \rightarrow [13, 14, 14] \rightarrow [13, 14] \rightarrow [15, 15] \rightarrow [15]$$

我们考虑输入的第一个例子。

最初，输入到该设备的数字数组为 $[6, 4, 8]$。它将按如下方式变化： $$[6, 4, 8] \rightarrow [4, 6, 8] \rightarrow [7, 8, 9] \rightarrow [10, 10, 10] \rightarrow [10]$$

接着，输入到该设备的数字数组为 $[6, 10, 8]$。它将按如下方式变化： $$[6, 10, 8] \rightarrow [6, 8, 10] \rightarrow [9, 10, 11] \rightarrow [12, 12, 12] \rightarrow [12]$$

最后，输入到该设备的数字数组为 $[6, 10, 1]$。它将按如下方式变化： $$[6, 10, 1] \rightarrow [1, 6, 10] \rightarrow [4, 8, 11] \rightarrow [7, 10, 12] \rightarrow [10, 12, 13] \rightarrow [13, 14, 14] \rightarrow [13, 14] \rightarrow [15, 15] \rightarrow [15]$$