Arithmetic Progression Queries Problem Statement

Given an integer array ARR of size N, perform the following operations:

- update(l, r, val): Add (val + i) to arr[l + i] for all 0 ≤ i ≤ r - l.

- rangeSum(l, r): Return the sum of all elements in the array from index l to r, i.e., the sum of arr[l...r].

Two types of queries denote these operations:

Type 1: For update(l, r, val) operation.
Type 2: For rangeSum(l, r) operation. 
Note: Queries use 1-based indexing.

Input:

Two integers N and Q representing the size of the array and number of operations.
The next Q lines contain operations, each starting with an integer representing the type of operation.
If the integer is 1, it describes a update(l, r, val) operation followed by integers l, r, and val.
If the integer is 2, it describes a rangeSum(l, r) operation followed by integers l and r.

Output:

For each operation of type 2, output the sum of arr[l..r] on a new line.

Example:

Input: 
N = 5, Q = 3
Operations: 
1 1 3 2
2 1 3
2 2 5

Output: 
6
15

Constraints:

• 1 ≤ N ≤ 10^5
• 1 ≤ Q ≤ 10^5
• 1 ≤ l ≤ r ≤ N
• 0 ≤ val ≤ 10^6
• 0 ≤ arr[i] ≤ 10^6

Note: The solution handles all input/output; just focus on implementing the function logic.