Problem - Polynomial Queries

Given an array of $n$ integers and $q$ queries:

$1.$ Update: add $1, 2, 3, ..., (r-l+1)$ to positions $l, l+1, ..., r$

$2.$ Query: return $sum(l, r)$ Constraints: $n, q \leq 2 \cdot 10^5$. This is a challenge for both segment trees and sqrt decomposition. The update isn't uniform, it's a polynomial pattern. Think about what you need to store per block to handle this efficiently.