Minimized Maximum of Products Distributed to Any Store

You are given an integer `n` indicating there are `n` specialty retail stores. There are `m` product types of varying amounts, which are given as a **0-indexed** integer array `quantities`, where `quantities[i]` represents the number of products of the `ith` product type. You need to distribute **all products** to the retail stores following these rules: - A store can only be given **at most one product type** but can be given **any** amount of it. - After distribution, each store will have been given some number of products (possibly `0`). Let `x` represent the maximum number of products given to any store. You want `x` to be as small as possible, i.e., you want to **minimize** the **maximum** number of products that are given to any store. Return _the minimum possible_ `x`.   **Example 1:** **Input:** n = 6, quantities = [11,6] **Output:** 3 **Explanation:** One optimal way is: - The 11 products of type 0 are distributed to the first four stores in these amounts: 2, 3, 3, 3 - The 6 products of type 1 are distributed to the other two stores in these amounts: 3, 3 The maximum number of products given to any store is max(2, 3, 3, 3, 3, 3) = 3. ``` **Example 2:** **Input:** n = 7, quantities = [15,10,10] **Output:** 5 **Explanation:** One optimal way is: - The 15 products of type 0 are distributed to the first three stores in these amounts: 5, 5, 5 - The 10 products of type 1 are distributed to the next two stores in these amounts: 5, 5 - The 10 products of type 2 are distributed to the last two stores in these amounts: 5, 5 The maximum number of products given to any store is max(5, 5, 5, 5, 5, 5, 5) = 5. ``` **Example 3:** **Input:** n = 1, quantities = [100000] **Output:** 100000 **Explanation:** The only optimal way is: - The 100000 products of type 0 are distributed to the only store. The maximum number of products given to any store is max(100000) = 100000. ```   **Constraints:** - `m == quantities.length` - `1 <= m <= n <= 105` - `1 <= quantities[i] <= 105`