In the contest, I tried implementing the Segment tree and thought the prefix array won't pass the time constraints, but I was wrong, here is my segment tree AC solution although it can be further optimized.

https://mirror.codeforces.com/contest/1843/submission/210506220

Also I didn't quite get wym by " check there at least on segment available " ??

in the contest, I tried to implement dfs using the prefix sum but it gives the wrong answer. Here is a perfect solution using a segment tree 210533304

you don't need segment trees for this... its just a basic binary search

Why learning segment trees when you haven't even solved 1300-Rated problems ?

If you're curious, this is a working solution with binary search and prefix sums — no segtree needed, and takes only ~60ms and 1.5MB: 210537397

Why do you learn Segment Tree? Go learn Binary Search.

In fact Binary Search was the expected solution, stop overcomplicating your solutions using hard algorirthms.

If you are interested in the range update method of solving the problem but you need an easy way to do this, I recommend the square root algorithm. It's more suited for beginners, and it is what I used in the contest.