2064 - Minimized Maximum of Products Distributed to Any Store\.

Medium

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 <code>i^th</code> 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

• <code>1 <= m <= n <= 10⁵</code>

• <code>1 <= quantitiesi<= 10⁵</code>