Difference Array Insight

To add $v$ to all elements from index $l$ to $r$, you only need to modify two positions in the difference array: $diff[l] += v$ $diff[r+1] -= v$ That's it.

Two operations, regardless of how big the range is. Why does this work?

When you later compute the prefix sum of $diff$, adding $v$ at position $l$ propagates forward to all later positions. Subtracting $v$ at $r+1$ cancels it for positions after $r$.