codeforces#P1862G. The Great Equalizer
The Great Equalizer
Description
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:
- Sort the current array in non-decreasing order and remove duplicate elements leaving only one occurrence of each element.
- 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.
- 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.
- 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:
- Assign the value $x$ ($1 \le x \le 10^9$) to the element $a_i$ ($1 \le i \le n$).
- 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.
Input
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 $2 \cdot 10^5$.
Output
For each test case, output $q$ integers — the output values of the device after each operation.
4
3
2 4 8
3
1 6
2 10
3 1
5
1 2 2 2 2
1
5 3
2
5 6
7
1 2
1 7
1 7
2 5
1 2
2 7
2 2
5
2 5 1 10 6
10
1 7
4 8
2 5
1 4
2 8
3 4
1 9
3 7
3 4
3 1
10 12 15
4
10 8 8 9 8 12 2
14 12 12 11 11 10 11 10 11 14
Note
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: $$[6, 10, 1] \rightarrow [1, 6, 10] \rightarrow [4, 8, 11] \rightarrow [7, 10, 12] \rightarrow [10, 12, 13] \rightarrow [13, 14, 14] \rightarrow [13, 14] \rightarrow [15, 15] \rightarrow [15]$$