After receiving yet another integer array $$$a_1, a_2, \ldots, a_n$$$ at her birthday party, Index decides to perform some operations on it.

Formally, there are $$$m$$$ operations that she is going to perform in order. Each of them belongs to one of the two types:

$$$\texttt{+ l r}$$$. Given two integers $$$l$$$ and $$$r$$$, for all $$$1 \leq i \leq n$$$ such that $$$l \leq a_i \leq r$$$, set $$$a_i := a_i + 1$$$.
$$$\texttt{- l r}$$$. Given two integers $$$l$$$ and $$$r$$$, for all $$$1 \leq i \leq n$$$ such that $$$l \leq a_i \leq r$$$, set $$$a_i := a_i - 1$$$.

For example, if the initial array $$$a = [7, 1, 3, 4, 3]$$$, after performing the operation $$$\texttt{+} \space 2 \space 4$$$, the array $$$a = [7, 1, 4, 5, 4]$$$. Then, after performing the operation $$$\texttt{-} \space 1 \space 10$$$, the array $$$a = [6, 0, 3, 4, 3]$$$.

Index is curious about the maximum value in the array $$$a$$$. Please help her find it after each of the $$$m$$$ operations.

Input

Each test consists of multiple test cases. The first line contains a single integer $$$t$$$ ($$$1 \leq t \leq 2 \cdot 10^4$$$) — the number of test cases. The description of the test cases follows.

The first line of each test case contains two integers $$$n$$$ and $$$m$$$ ($$$1 \leq n \leq 10^5$$$, $$$1 \leq m \leq 10^5$$$) — the length of the array and the number of operations.

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

Then $$$m$$$ lines follow, each line corresponds to the operation, in the following format: $$$\texttt{c l r}$$$ ($$$c \in \{\texttt +, \texttt -\}$$$, $$$l$$$ and $$$r$$$ are integers, $$$1 \leq l \leq r \leq 10^9$$$) — the description of the operation.

Note that the elements $$$a_i$$$ may not satisfy $$$1\le a_i\le 10^9$$$ after some operations, as it is shown in the example.

It is guaranteed that the sum of $$$n$$$ over all test cases does not exceed $$$10^5$$$, and the sum of $$$m$$$ over all test cases does not exceed $$$10^5$$$.

Output

For each test case, output one single line containing $$$m$$$ integers, with the $$$i$$$-th of them describing the maximum value of the array after the $$$i$$$-th operation.

Note

In the first test case, the process of the operations is listed below:

After the first operation, the array becomes equal $$$[2,3,4,3,2]$$$. The maximum value is $$$4$$$.
After the second operation, the array becomes equal $$$[1,2,4,2,1]$$$. The maximum value is $$$4$$$.
After the third operation, the array becomes equal $$$[2,3,4,3,2]$$$. The maximum value is $$$4$$$.
After the fourth operation, the array becomes equal $$$[3,4,5,4,3]$$$. The maximum value is $$$5$$$.
After the fifth operation, the array becomes equal $$$[3,4,5,4,3]$$$. The maximum value is $$$5$$$.

In the second test case, the process of the operations is listed below:

After the first operation, the array becomes equal $$$[2,4,4,5,5]$$$. The maximum value is $$$5$$$.
After the second operation, the array becomes equal $$$[3,4,4,5,5]$$$. The maximum value is $$$5$$$.
After the third operation, the array becomes equal $$$[3,3,3,4,4]$$$. The maximum value is $$$4$$$.
After the fourth operation, the array becomes equal $$$[2,2,2,4,4]$$$. The maximum value is $$$4$$$.
After the fifth operation, the array becomes equal $$$[1,1,1,3,3]$$$. The maximum value is $$$3$$$.

Idx	Name	Rating
A	Dora's Set	800
B	Index and Maximum Value	900
C	Dora and C++	1500

Codeforces Round 969 (Div. 2)