Smallest Square 2

There are $N$ points on the coordinate plane. Every point has integer coordinates.

Consider the squares that satisfy all three conditions below.

• All four corners have integer coordinates.
• Every side is parallel to a coordinate axis.
• At least $K$ points lie strictly inside the square. A point on the boundary does not count as being inside.

Write a program that finds the smallest area among these squares.

The first line contains the number of points $N$ and an integer $K$. ($2 \le N \le 100$, $1 \le K \le N$)

Each of the next $N$ lines contains the coordinates $x$ and $y$ of one point, separated by a space. ($-10^9 \le x, y \le 10^9$)

No point is given more than once.

Print the smallest area among the squares that satisfy the conditions.