Problem:
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.

Sample Input 1

4 4
1 4
3 3
6 2
8 1

Sample Output 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.

Sample Input 2

4 2
0 0
1 1
2 2
3 3

Sample Output 2

1

Sample Input 3

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

Sample Output 3

3999999996000000001

Watch out for integer overflows.

Solution in Go (1.14.1) (judge verdict: Wrong Answer)

package main

import (
	"fmt"
)

func main() {
	var n, K int
	fmt.Scan(&n, &K)

	ps := make([]Point, n)
	var x, y int
	for i := 0; i < n; i++ {
		fmt.Scan(&x, &y)
		ps[i] = Point{i, x, y}
	}

	ans := int(1e18 * 4)
	for i := 0; i < n; i++ {
		for j := 0; j < n; j++ {
			for k := 0; k < n; k++ {
				p1, p2, p3 := ps[i], ps[j], ps[k]
				x1 := min(p1.x, min(p2.x, p3.x))
				y1 := min(p1.y, min(p2.y, p3.y))
				x2 := max(p1.x, max(p2.x, p3.x))
				y2 := max(p1.y, max(p2.y, p3.y))

				cnt := 0
				for _, p := range ps {
					if x1 <= p.x && p.x <= x2 && y1 <= p.y && p.y <= y2 {
						cnt++
						if K <= cnt {
							ans = min(ans, (x2-x1)*(y2-y1))
							break
						}
					}
				}
			}
		}
	}

	fmt.Println(ans)
}

// Point .
type Point struct {
	i, x, y int
}

func min(a, b int) int {
	if a < b {
		return a
	}
	return b
}

func max(a, b int) int {
	if a > b {
		return a
	}
	return b
}