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D - Axis-Parallel Rectangle

Score : $400$ points

Problem Statement

We have $N$ points in a two-dimensional plane.
The coordinates of the $i$-th point $(1 \leq i \leq N)$ are $(x_i,y_i)$.
Let us consider a rectangle whose sides are parallel to the coordinate axes that contains $K$ or more of the $N$ points in its interior.
Here, points on the sides of the rectangle are considered to be in the interior.
Find the minimum possible area of such a rectangle.

Constraints

• $2 \leq K \leq N \leq 50$
• $-10^9 \leq x_i,y_i \leq 10^9 (1 \leq i \leq N)$
• $x_i≠x_j (1 \leq i<j \leq N)$
• $y_i≠y_j (1 \leq i<j \leq N)$
• All input values are integers. (Added at 21:50 JST)

Input

Input is given from Standard Input in the following format:

$N$ $K$

$x_1$ $y_1$

$:$

$x_{N}$ $y_{N}$

Output

Print the minimum possible area of a rectangle that satisfies the condition.

4 4
1 4
3 3
6 2
8 1

21

One rectangle that satisfies the condition with the minimum possible area has the following vertices: $(1,1)$, $(8,1)$, $(1,4)$ and $(8,4)$.
Its area is $(8-1) × (4-1) = 21$.

4 2
0 0
1 1
2 2
3 3

1

4 3
-1000000000 -1000000000
1000000000 1000000000
-999999999 999999999
999999999 -999999999

3999999996000000001

Watch out for integer overflows.