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 Kotlin (1.0.0) (judge verdict: Accepted)

fun main(args: Array<String>) {
    val (n, k) = readStrings().map(String::toInt)
    val pointList = arrayListOf<Point>()
    for (i in 1..n) {
        val (x, y) = readStrings().map(String::toInt)
        pointList.add(Point(x, y))
    }

    val verticalSorted = pointList.sortedBy { it.y }
    val horizontalSorted = pointList.sortedBy { it.x }

    var ans = Long.MAX_VALUE
    for (left in horizontalSorted) {
        for (right in horizontalSorted) {
            if (left.x >= right.x) {
                continue
            }

            for (top in verticalSorted) {
                if (!(top.x in left.x..right.x)) {
                    continue
                }

                for (bottom in verticalSorted) {
                    if (top.y >= bottom.y ||
                        !(bottom.x in left.x..right.x)) {
                        continue
                    }

                    val includedCount = pointList.count {
                        it.x in left.x..right.x
                        && it.y in top.y..bottom.y
                    }

                    if (includedCount < k) {
                        continue
                    }

                    ans = Math.min(ans, (right.x - left.x).toLong() * (bottom.y - top.y).toLong())
                }
            }
        }
    }

    println(ans)
}

fun readStrings() = readLine()!!.split(" ")


data class Point(val x: Int, val y: Int)