Optimal Consumption Rate

A resource processor needs to consume materials from multiple stockpiles before an external event occurs. There are n stockpiles of materials, where the i-th stockpile contains stockpiles[i] units of material. The processor has a limited time window of deadline hours before the event.

The processor operates at a fixed consumption rate of k units per hour. During each hour, the processor selects one stockpile and consumes up to k units from it. If a stockpile contains fewer than k units remaining, the processor consumes all remaining units from that stockpile and idles for the remainder of that hour (it cannot switch to another stockpile mid-hour).

The processor prefers to operate at a slower, more energy-efficient rate while still completing all consumption before the deadline.

Your task is to determine the minimum integer consumption rate k such that the processor can consume all materials from all stockpiles within the given deadline hours.