You are given an integer n representing the number of retail stores and an integer array quantities, where quantities[i] denotes the total quantity of the $i$-th product type.

You must distribute all products to the n stores adhering to the following rules:

• A store can be allocated at most one product type, but can receive any amount of that product.

• A store may also receive $0$ products.

Let $x$ be the maximum number of products allocated to any single store.

Return the minimum possible value of $x$.

Constraints:

• m $==$ quantities.length

• $1 \leq$ m $\leq$ n $\leq 10^5$

• $1 \leq$ quantities[i] $\leq 10^5$

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.