Maximum subarray sum with length limits

You are given an array of $n$ integers. Find the maximum sum of a subarray whose length is between $a$ and $b$.

The first line contains $n$, $a$, $b$ ($1 \le a \le b \le n \le 2 \cdot 10^5$). The second line contains $n$ integers ($|x_i| \le 10^9$).

A single number — the maximum sum.

The sum of $[l, r]$ is $p_r - p_{l-1}$, and the length condition is $r - b \le l - 1 \le r - a$. So for every $r$ you need the minimum prefix in the window $p_{r-b}, \ldots, p_{r-a}$ — a sliding window minimum. Keep it in a monotonic deque with amortised $O(1)$ per step (or a multiset with $O(\log n)$).

Scanning the window for every $r$ is $O(n(b - a))$ — too slow when $b - a$ is large. In the example $5 + 3 = 8$.

Source: CSES, problem 1644.