Magnetic Force Between Two Balls

Statement

In the universe Earth C-137, Rick has discovered a unique type of magnetic force between two balls when placed in his newly invented baskets. He has $n$ baskets, each located at specific positions given by the array position[i]. Morty has m balls and needs to distribute these balls across the baskets in such a way that the minimum magnetic force between any two balls is as large as possible.

The magnetic force between two balls placed at positions $x$ and $y$ is calculated as the absolute difference $|x−y|$.

Given an integer array position and the number of balls m, return the maximum possible value of the minimum magnetic force between any two balls after they have been placed in the baskets.

Constraints:

• $2 \leq$ position.length $\leq 10^3$

• $1 \leq$ position[i] $\leq 10^4$

• All integers in position are unique.

• $2 \leq$ m $\leq$ position.length

Examples