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.

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 $ .

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

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] $ $$$