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 Scala (2.11.7) (judge verdict: Time Limit Exceeded)

import java.io._
import java.util.StringTokenizer
import scala.util.control.Breaks.{breakable,break}

object Main extends App {
  val in = new InputReader(System.in)
  val pw = new PrintWriter(System.out)

  type IP = (Int, Int)

  def check(p: IP, ps: IP, pl: IP): Boolean = {
    val (nx, ny) = p
    ps._1 <= nx && nx <= pl._1 && ps._2 <= ny && ny <= pl._2
  }


  val N, K = in.next().toInt
  val pos = new Array[IP](N)
  var xs = new Array[Int](N)
  var ys = new Array[Int](N)

  for(i <- 0 until N) {
    val x, y = in.next().toInt
    pos(i) = (x, y)
    xs(i) = x
    ys(i) = y
  }

  xs = xs.sorted
  ys = ys.sorted

  var ans: Long = Long.MaxValue

  for(ix <- 0 until N; jx <- 0 until N; iy <- 0 until N; jy <- 0 until N) {
    val hoge =
      pos
        .filter(check(_, (xs(ix), ys(iy)), (xs(jx), ys(jy))))
        .length
    if(hoge >= K)
      ans = Math.min(ans, (xs(jx).toLong-xs(ix))*(ys(jy)-ys(iy)))
  }
  println(ans)
}


class InputReader(stream: InputStream) {
  private val reader = new BufferedReader(new InputStreamReader(stream))
  private var tokenizer: StringTokenizer = new StringTokenizer(reader.readLine())
  def next(): String = {
    while (!tokenizer.hasMoreTokens()) {
      tokenizer = new StringTokenizer(reader.readLine())
    }
    tokenizer.nextToken()
  }
}