Minimum Threshold for Resource Allocation Solution

Problem Statement

You are given an array of positive integers `rates` of length `n`, and an integer `k`. You need to find the minimum positive integer threshold `M` such that the sum of ceil(rates[i] / M) for all 0 <= i < n is less than or equal to `k`. Here, ceil(x) represents the ceiling function, which returns the smallest integer greater than or equal to x. If no such positive integer `M` exists (which occurs when `k` is less than `n`), return -1.

Constraints

• 1 <= rates.length <= 10^5
• 1 <= rates[i] <= 10^9
• 1 <= k <= 10^9

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