Garden Operations

You are given a garden with n plots, numbered from 1 to n, and each plot has an initial height. You will be asked to perform m operations on this garden. There are two types of operations:

• Type 1 (Update): 1 l r h. Increase the height of every plot from index l to r by h. Mathematically, for each i such that
  \( l \le i \le r \), update \( h_i \) as follows:
  \( h_i = h_i + h \).</p>
• Type 2 (Query): 2 l r. Query the maximum height among plots from index l to r. That is, output \( \max\{h_l, h_{l+1}, \ldots, h_r\} \).

It is guaranteed that the input operations will be valid. For operations of type 2, output the result on a new line. Note that if there are no query operations, nothing should be printed.

inputFormat

The first line contains two space-separated integers n and m — the number of plots and the number of operations respectively.

The second line contains n space-separated integers representing the initial heights of the plots.

Each of the following m lines contains an operation in one of the following forms:

• 1 l r h — increase the heights of plots from l to r by h.
• 2 l r — query and output the maximum height among plots from l to r.

outputFormat

For each query operation (type 2), output the maximum height in the specified interval on a new line. If there are no query operations, output nothing.

## sample

6 5
1 2 3 4 5 6
2 1 6
1 2 4 2
2 2 5
1 1 3 1
2 1 3

6
6
6

</p>