Dossiers Priority Manager

In this problem, you are given an array of integers representing the priority levels of dossiers. You will then be given a series of operations to perform on this array. The operations are as follows:

1. Increment Operation: Increase all elements in the index range $[l, r]$ by a value $x$.
2. Decrement Operation: Decrease all elements in the index range $[l, r]$ by a value $x$.
3. Query Operation: Output the maximum value in the index range $[l, r]$.

Note that the array is 1-indexed. You are required to process the queries in order and output the result of each query operation (type 3) on a separate line.

The input is read from standard input (stdin) and the results should be printed to standard output (stdout).

inputFormat

The first line contains two integers $n$ and $q$, representing the number of dossiers and the number of operations, respectively. The second line contains $n$ space-separated integers, representing the initial priority levels of the dossiers. The next $q$ lines each describe an operation in one of the following formats:

• For the increment operation: 1 l r x
• For the decrement operation: 2 l r x
• For the query operation: 3 l r

Here, $l$ and $r$ (with $1 \leq l \leq r \leq n$) denote the start and end indices of the range (inclusive), and $x$ is the value to add or subtract.

outputFormat

For each query operation (operation type 3), output a single line containing the maximum dossier priority in the specified range.## sample

10 5
5 3 8 1 6 4 9 2 7 5
1 3 7 2
2 2 5 1
3 1 7
1 6 10 5
3 6 10

11
16