Maximize minimum value after k decrements

You are given an integer array `vulnerabilities` of length `n`, where `vulnerabilities[i]` is the initial security score of server `i`. You must perform exactly `k` operations. In each operation, choose any server `i` and decrease `vulnerabilities[i]` by `1`. After all `k` operations, let the resulting array be `final`. **Task**: Compute the maximum possible value of `min(final)` that you can achieve by choosing which servers to decrement each time. ### Input - Integer array `vulnerabilities` (length `n`) - Integer `k` (number of operations) ### Output - An integer: the maximum achievable `min(final)` ### Notes / Constraints (reasonable interview assumptions) - `1 ≤ n ≤ 2e5` - `0 ≤ vulnerabilities[i] ≤ 1e9` - `0 ≤ k ≤ 1e12` - Decrements may make values negative. ### Example - `vulnerabilities = [5, 1, 4]`, `k = 3` - One optimal strategy is to decrement the `5` three times → `[2, 1, 4]`, so `min = 1`. - Output: `1`