Shortest Subarray - The Idea

The sum of subarray from $i+1$ to $j$ is $prefix[j] - prefix[i]$. You want this to be at least $k$.

For each $j$, you're looking for the largest $i < j$ such that $prefix[j] - prefix[i] \geq k$, which means $prefix[i] \leq prefix[j] - k$.

If $prefix[i_1] \geq prefix[i_2]$ where $i_1 < i_2$, then $i_1$ is never useful. Any $j$ that could use $i_1$ could use $i_2$ instead and get a shorter subarray. This "dominated" insight means you can use a monotonic deque.