Shortest Subarray - Prefix Sums

Let $P[i]$ = sum of first $i$ elements, with $P[0] = 0$. The sum of subarray $[i, j)$ is $P[j] - P[i]$. You want $P[j] - P[i] \geq k$ with $j > i$, reducing $j - i$. Rearranging: $P[j] - k \geq P[i]$. For each $j$, you're looking for the largest $i < j$ such that $P[i] \leq P[j] - k$.

But you also want $j - i$ as small as possible, which means you want $i$ as large as possible while still satisfying the constraint.