Challenge: Negative Values

With all non-negative values, sliding window (two pointers) finds shortest subarray with sum $\geq K$ in $O(n)$. Negative values break monotonicity of cumulative sums.

Expanding the window can decrease the sum. Prefix sums + monotonic queue handle this. We maintain increasing prefixes because larger prefixes are better left bounds. observation: if $prefix[i] \geq prefix[j]$ for $i < j$, then $i$ is never a better left bound than $j$ for any future right bound.