Saturated Subarrays

For an array $B$ of length $M$, let $f(B)$ denote its maximum subarray sum. Note that in this problem, the empty subarray with a sum of $0$ is considered to be a subarray of $B$. We say the array $B$ is *saturated* if $f(B) = \sum_{i=1}^M B_i$, that is, if the maximum subarray sum of $B$ equals the sum of $B$. You're given an array $A$ of length $N$. Answer $Q$ queries on it of the following f