Shortest Subarray - Walkthrough

Find shortest subarray with sum $\geq K$. Use prefix sums: $sum[l..r] = prefix[r+1] - prefix[l] \geq K$. We want $prefix[r+1] - prefix[l] \geq K$, i.e., $prefix[l] \leq prefix[r+1] - K$.

For each $r$, find smallest valid $l$. Maintain monotonic increasing deque of prefix indices. For each $r$, pop front while $prefix[front] \leq prefix[r] - K$. After popping, if queue non-empty, the popped indices give valid subarrays. Track minimum length. Also pop back if $prefix[r] \leq prefix[back]$.